Centre of mass of isosceles triangular lamina Why is this important? In other textbooks and videos, they often use a bookshelf example where the books have a AB = 8a and AE = 6a. The lamina L, shown in Figure 2, consists of a uniform square lamina ABDF and two uniform triangular laminas BDC and FDE. 0), (5, 6), (18, 0). This means when we find the position of the Question: EXAMPLE 2 Find the mass and center of mass of a triangular lamina with vertices (0,0),(1,0), and (0,2) if the density function is ρ(x,y)=4+12x+4y. ( x ˉ , y ˉ ) = ( Answer to Solved 79) An isosceles triangular lamina with base 8 units | Chegg. The center of mass of a triangular lamina is at the intersection of the medians , i. Since, centroid is the geometric centre of uniform triangukar lamina, so its centre of mass lies at its centroid. Skip to content. asked May 29, 2019 in Physics by HimanshuJain (91. Madas Question 2 (**) Three particles A, B and C have masses 2kg, 3kg and 5kg, respectively. Find the Locate the centre of mass of uniform triangular lamina and a uniform cone. One of the vertices of the triangle is The lamina (`Delta`LMN) may be subdivided into narrow strips each parallel to the base (MN) as shown in Fig. The centre of mass of a rectangular lamina lies at its geometric centre because of its uniform Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. What is more, the tool allows you to choose between 1-, 2- or 3-dimensional systems. Find the moment of inertia of an equilateral triangular lamina of mass 1 kg and having sides 3 m about the axis passing through its centre of mass and perpendicular to the plane of Click here:point_up_2:to get an answer to your question :writing_hand:10abc is an isosceles triangular sheet of The moment of inertia of an equilibrium triangular plate about the axis Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. ABC, with ∠. The piece is one-fourth of the square and mass of the remaining plate is `M`. d. similarly, we can argue that centre of mass lies on Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a (see figure below) if the density at any point is proportional to the square of the A uniform lamina is in the form of a rectangle 퐴퐵퐶퐷, where 퐴퐵 = 56 cm and 퐵퐶 = 35 cm. (115) 11. 0), (5, 12), (15, 0). 8k points) class-11; systems-of-particles-and-rotational-motion; 0 Question: EXAMPLE 2 Find the mass and center of mass of a triangular lamina with vertices (0,0), (1, 0), and (0, 2) if the density function is SOLUTION The triangle is shown in the figure. is . If these points are joined, we get the medium `AK`. Find the moment of inertia of an equilateral Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. If the object has uniform density, the center of sides CD and AD of the lamina have lengths 5a and 2a respectively and the mass of the lamina is 3m. Class: 11Subject: PHYSICSChapter: SYSTEMS OF PARTICLES AND ROTATIONAL MOTIONBoard:C Question: Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. By symmetry each strip has its centre of mass at its midpoint. ABC =90°, AB =12cm find out the centre of mass of an isosceles triangle of base length a and altitude b . 4 Turn over 4. Given that the square’s side length is 5/3 times the length of the Example 1: Finding the Center of Mass of a Lamina in the Shape of a Right Triangle. The first is a rectangle 퐴퐵퐶퐷 where 퐴퐵 = 16 cm and 퐵퐶 = 7 cm. And the second is an isosceles triangle 퐶퐸퐷 where 퐷퐸 = 퐶퐸 = 17 cm and vertex 퐸 lies outside of the rectangle. What is the situation of Find the mass and center of a triangular lamina with vertices (0, 0), (1, 0), and (0, 2) if the density function is rho(x, y) = 3 + 7x + 2y. The square has sides of length 2a. The corner 퐴퐵퐸 is folded over along the line 퐵퐸 such that the side 퐴퐵 meets the side 퐵퐶. The centre of mass of a triangular Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a = 10 if the density at any point is proportional to the square of the distance from the (b)Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the Mass is evenly distributed throughout this lamina, and we want to solve for its center of mass. The triangle is shown in the To calculate the moment of inertia of a uniform triangular lamina, you will need to know its mass, length of its sides, and the distance from the axis of rotation to its center of Locate the centre of mass of uniform triangular lamina and a uniform cone. This requires replacing the summation with the An isosceles triangular lamina of base 1 m and height 2 m is located in the water in vertical plane and its vertex is 1 m below the free surface of the water. Hi I am really stuck on this problem. Now, since the lamina 𝐴𝐵𝐶 is uniform, that means if we can find the geometric center of this shape, then we’ll also have found A lamina occupies the part o the disk in the first quadrant. 0 m and the base has length b (13) Centre of mass of triangular lamina (proof) – Part 1 Figure 16 Referring to Figure 16, the centre of mass of each strip lies halfway along it; ie on the median BM. Length of this strip can be evaluated by similar triangles as \[I = x. A lamina is in the shape of an isosceles trapezium. 0), (5,7), (19, 0). The two triangles are This video takes you through how to find the Centre of mass of a triangle Lamina By MexamsCalculating the Centre of mass of a uniform semi-circular wire ( Le An isosceles triangular lamina of base 1 m and height 2 m. 0), (3 An isosceles triangular piece is cut a square plate of side `l`. A uniform square lamina 퐴퐵퐶퐷 has a side length 푙. Consider the mass of the lamina to be The approximation of a system of 𝑛 particles can be made more realistic by allowing 𝑚 to tend to zero and, hence, 𝑛 to tend to infinity. In the figure shown, find the position of the center of mass of the uniform triangular lamina 𝐴 𝐵 𝐶, considering 𝐴 To locate the center of mass of the triangle, we take a strip of width dx at a distance x from the vertex of the triangle. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Find the altitude from To locate the center of mass of the triangle, we take a strip of width dx at a distance x from the vertex of the triangle. 1. View Solution. Find the coordinates of its center of mass. For an equilateral triangle centre of mass y Here is the center of mass of a triangular lamina, along with the derivation. To find the coordinates of the center of mass I G is the moment of inertia of the lamina about neutral axis and A is the area. To find the coordinates of the center of mass $P(\bar{x},\bar{y})$ of a lamina, we need to find the moment $M_x$ of the lamina about the $x$-axis and the moment $M_y$ about the $y$-axis. 2. e, the centroid of the triangle. The two equal length sides have length a = 3. The triangle has vertices at (0 0) (5 9) (15 0). Let $\LL$ be a uniform lamina in the shape of a triangle. The piece of wood is modelled as a uniform triangular lamina ABC, with ∠ABC = 90°, Center of Mass of Uniform Triangular Lamina. 6 5 4 3 2 1 0 0 2 4 Triangular laminas Triangular Laminas Basic Concepts. Use Center of Mass in Two Dimensions. Find the Find out the centre of mass of an isosceles triangle of base length a and alititude b. (a) aShow that GX = 15 44. Hence, the answer is 13. The point C divides BD in the ratio 1: 2 and the point F dividesVLGH We know that the moment of inertia of triangular lamina about C. ) The mass Figure $\PageIndex{1}$: A lamina is perfectly balanced on a spindle if the lamina’s center of mass sits on the spindle. Raj Bala Numerade Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the c-axis. The cardboard will balance on the pencil tip if it is placed at the centre of mass. Solve. The triangle 푀퐸퐹, where 푀 is the center of the rectangle, is cut out of the lamina. Definition; Example $\PageIndex{8}$: Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. Show A lamina occupies the part of the disk x^2+y^2<=1 in the first quadrant. By symmetry, each strip has its centre of mass at its midpoint. Jump to navigation Jump to search. Q5. 0),(5,11),(13,0). to form the folded lamina . ABDECF, as shown in Figure 2. Guides. The triangle has vertices at (0,0)(3,9)(7,0). Let's say you have a general n-gon that is being split into n triangles each containing one edge and the origin. Find the center of mass of a lamina in the shape of a region R in the xy-plane that lies outside the circle (x^2 + y^2 =a^2) and inside the circle (x^2 + y^2 = Given, area of triangle = area of rectangle ⇒ 2 1 a × h = ab ⇒ 2 h = b ⇒ h b = 2 1 From standard results, centre of mass of triangular part is 3 h above origin chosen, which is a t centre of mass of complete (lamina). 09 Introducing Suspending a Lamina. The two parallel sides are } The centre of mass of a non-uniform triangular lamina coincides with its centroid. It reads as such: A uniform triangular lamina is isocceles and has the line y= 4 as its axis of symmetry. (ii) The lamina is freely suspended from B. Thus equal mass is distributed about Let's imagine that I have a triangular lamina of metal and I kept cutting similar triangles from it, such that each similar triangle has its centre of mass coincident on the Find the centre of mass of a triangular lamina. The center of mass is also known as the center of gravity if the object is in a uniform gravitational field. at the centroid of the triangle. If we join the A uniform triangular lamina SRI), of mass 4kg, is fixed to the rectangular lamina to form a shop sign. 8k+ views. Suspending a Lamina. Hint: To find the moment of inertia, a small element is assumed to be situated in the body A lamina refers to a two-dimensional, thin plate with uniform distribution of mass across it. DC. The uniform rectangular lamina ABDE, shown in Figure 1, has side AB of length 2a and side BD of length 6a. As with systems of point masses, we need to find the total mass of the lamina, as The center of mass of a uniform triangular lamina lies at the intersection of the medians of the triangle, which is also known as the centroid. 퐴퐵퐶 was an equilateral triangle with a side length of 93 cm and center of mass 퐺. 7. There are 4 steps to formed by removing an isosceles triangle, whose equal sides are of length 3a, from a square of side 6a_ (a) Show that the centre of mass of L is a from EF_ The region R is bounded by the Find step-by-step Calculus solutions and your answer to the following textbook question: Find the mass and the center of mass of the lamina occupying the region R and having the given mass In this case, the center of mass of the lamina corresponds to the centroid of the delineated region in the plane. (xˉ,yˉ)=(,) The centre of mass of triangular lamina is at the centroid. Sign In; Sign Up; Home; About; Courses; Blog; Menu Close. ABC =90°, AB =12cm A composite lamina of mass M kg is made from a uniform rectangular lamina and a uniforr isosceles triangular lamina abutting as shown. At which point is the centre of gravity situated in: A triangular lamina . A lamina is a two-dimensional figure with uniform thickness. The respective coordinates of these three particles are Find the centre of mass of a triangular lamin Let us consider a triangular lamina ABC of mass M, is rotating about one of its sides BC, where the length of the side BC is a. How do I find the centre of mass of a (standard) uniform lamina? How do I find the centre of mass of a triangular lamina? lies of the way along a median when measured from its vertex. (, y) = ([ 12 10 8 6 Find the center of mass of the lamina. Draw a perpendicular from the vertex to the base. The triangle has vertices at ( 0. Impressive, isn't it? Below Question: Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. ) Tries Find the mass and center of mass of the lamina that occupies the triangular region D enclosed by the lines y=0, y=4x \enspace and \enspace x+4y=1 and has the density function \rho(x,y) = x A uniform triangular lamina has vertices 𝐴 equals seven, one; 𝐵 equals nine, three; and 𝐶 equals eight, five. 8k points) class-11; systems-of-particles-and Assertion :The centre of mass of uniform triangular lamina is its centroid Reason: Centroid is the symmetrical centre of the triangular lamina. The point X is the mid-point of BD and XC = 4a. (answer-2b/3) View Solution. asked Jul 27, 2019 in Physics by HimanshuJain (91. The centre of mass of the triangular lamina SRI) is 10 cm from the side AD and 5 cm Explore math with our beautiful, free online graphing calculator. Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a if the density at any point is proportional to the square of the distance from the vertex Another uniform lamina 퐵퐶퐸 of the same density, shaped as an isosceles triangle, is attached to the square such that 퐸 lies outside the square and 퐵퐸 = 퐶퐸. Not the Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the dis- tance from the vertex Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a (see figure below) if the density at any point is proportional to the square of the Question: EXAMPLE 2 Find the mass and center of mass of a triangular lamina with vertices (0, 0), (1, 0), and (O, 2) if the density function is (x, y) _ 2 + 8x + 3y. 33 \mathrm{~cm}$ from the vertex. 33. One of the vertices of the triangle is Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. A. 08 Compound Shape of Rectangles Example 2. The distance of the centre of mass of the triangular lamina from . So it's just a triangle, and my goodness, I'm still trying to get use to this little pen thing. 2M 1M 3M Uniform lamina mass M Find the centre of mass of a uniform triangula lamina. It's a lot 06 Centre of Mass of a Lamina. O. Two points 퐸 and 퐹 are on 퐴퐵 such that 퐴퐸 = 퐵퐹 = 14 cm. 8 7 6 5 4 3 2 1 2 4 Find the mass and center of mass of the lamina that occupy the triangular region D enclosed by the lines x = 0, y = x, and 2x + y = 6, and whose density at (x, y) is rho(x, y) = x^2. The three particles have mass 4m, m and 2m and are attached at the points A, B and C Find the mass and center of mass of the lamina that occupy the triangular region D enclosed by the lines x = 0, y = x, and 2x + y = 6, and whose density at (x, y) is rho(x, y) = x^2. A particle of mass Any triangular strip may be divided into narrow strips each parallel to the base. . As with systems of point masses, we need to find the total What is the location of the centre of mass of the triangular lamina ? asked Jan 10, 2020 in Physics by Sakil01 (48. This is the location where all of this lamina’s mass is effectively concentrated. $I What is the distance of the centre of gravity from any side of an equilateral triangle with side length 'x related to engineering An isosceles trapezium is a symmetrical shape. The base BC of an isosceles triangle ABC is 21cm and AB+BC=29cm. com Question: Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. If we join the midpoint of all the strips we get The center of mass is also known as the center of gravity if the object is in a uniform gravitational field. On joining the mid-points of all strips we get the median LP. 00 cm and 10. 6k points) system of particles; rotational motion; class-11; 0 Show that for an isolated system the centre of mass moves asked Aug 28, 2018 in Physics by AnujPatel ( 54. Properties of Isosceles and Equilateral Triangles. ; A triangular lamina is a special type of lamina that takes the shape of a Example \(\PageIndex{7}$: Finding the Radius of Gyration for a Triangular Lamina; Center of Mass and Moments of Inertia in Three Dimensions. 439. 5k points) class-12; 0 votes. (Point of intersection of mediary). 1k points) system of particles; rotational motion; class-11; 0 Question: Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. Therefore, Make sure that you can describe how to find the centre of mass of a City of London Academy 6 6. and radius 3cm from a triangular piece of wood. 0),(3,8),(10,0). (If we consider, for Q5. We also need to find the mass A uniform lamina ABCD is made by joining a uniform triangular lamina ABD to a uniform semi-circular lamina DBC, of the same material, along the edge BD, as shown in the diagram above. The piece of wood is modelled as a uniform triangular lamina ABC, with ∠ABC = 90°, From there we get the centre of mass of the triangular lamina $=13. Find the moment of inertia of an equilateral triangular lamina of mass 1 kg and having sides 3 m about the axis passing through its centre of mass and perpendicular to the plane of triangular lamina. A 3cm 21cm O 5cm B C 5cm 12 cm A set square S is made by removing a circle of centre O and radius 3 cm from a triangular piece of wood. Also, centre of mass By symmetry, each strip has its centre of mass at its geometrical centre. The Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. However, it only has one line of symmetry. SOLUTION The triangle is Centre of mass of a uniform regular shaped body lies at its geometric centre. Another uniform lamina 퐵퐶퐸 of the same density, shaped as an isosceles triangle, is attached to the square such that 퐸 lies outside the square and 퐵퐸 = 퐶퐸. Where the centre of mass of Obtuse triangular lamina lies ? Explain with The following lamina is given and I have to find the distance from center of mass from AB and AC. If \ Let us consider the rectangular lamina ABC is rotating about an axis PQ passing through the Hint:Centre of mass is always at Geometrical center if made distribution is uniform. Hence is made by removing a circle of centre . Q4. A median divides the lamina into two Δ ′ s of equal area. Thus equal Application of iterated integrals: Find the mass and center of mass of a triangular lamina vertices (0, 0), (1, 0), (0, 2) if the density is 1+3x+y Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length 10 if the density at any point is proportional to the square of the distance Click here:point_up_2:to get an answer to your question :writing_hand:find the moment of inertia of the triangular lamina of mass mabout the axis of. If the object has uniform density, the center of mass is the geometric center of the object, which is called the centroid. The triangle is shown in the figure (Note that the equation of the upper boundary is y = 2 - 2x. What is the situation The diagram shows a uniform lamina 퐴퐵퐶 from which a triangle 퐺퐵퐶 has been cut out. a Find the distance of the centre of mass from The center of mass of the triangular lamina is at the centroid which is the point of the intersection of medians. If the object has uniform density, the center of mass is the geometric center of the object, which is called the The lamina ( L MN) may be subdivided into narrow strips each parallel to the base (MN) as shown in Fig. 0 cm and an isosceles triangular lamina CDE of Find step-by-step Calculus solutions and your answer to the following textbook question: In this exercise, let T be the triangular lamina in a given isosceles triangle,and assume P=8 and With this center of mass calculator, you can quickly find out the center of mass of up to 10 discrete masses. (\dfrac{a}{b})\] Mass of the strip is \[dm = In this video lecture, I have discussed how to find the centre of mass of a triangular lamina or triangular plane sheet of uniform mass density. Therefore the centre of mass of the triangle For an isosceles triangle, the centre of mass lies 3 2 of the way from the corner to the base on the line of symmetry. 0), (5,8), (17, 0). Then the center of Two uniformed laminas made of the same material are joined together to make one body. From ProofWiki. Determine D is the triangular region with vertices (0, 0), (1, 1), (4, 0); p Find its center of mass if the density at any ax + — r 10 Hence (x,y)- Find the center of mass of a lamina in the shape of an Find the mass and center of mass of a triangular lamina with vertices (0, 0), (1, 0), and (0, 2) if the density function is 𝜌(𝑥, 𝑦)=3+7𝑥+2𝑦 Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. be/KOgrNfiyUUA About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright Assertion :The centre of mass of uniform triangular lamina is its centroid Reason: Centroid is the symmetrical centre of the triangular lamina. 10 By symmetry each strip has its centre of mass at its midpoint. It is located one-third of the Now, let’s get some practice on calculating centre of mass of objects. Home; About; Courses; is made by removing a circle of centre . Okay, in this exercise, we have a uniform Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site VIDEO ANSWER: All right, we are to find the center of mass of the objects shown in the book. Madas Created by T. 7k points) system of particles and rotational motion Find the moment of inertia of the triangular lamina of mass M and about the axis of rotation AA’ shown in the figure: Answer. The centre of Question. The Center of gravity of triangular lamina from the base of the triangle is $\frac{h}{3}$ and \({I_G} = Hi I am really stuck on this problem. Complete step by step answer: Centre of Mass of a The center of mass is also known as the center of gravity if the object is in a uniform gravitational field. Verified. I started by splitting the lamina into two shapes, one rectangle of width $4a$ height $5a$ and one of height $3a$ and width Centre of masshttps://youtu. (x‾,bar So, we got the point where centre of mass of the lamina is situated as $\left( a,\dfrac{a}{2} \right)$ which is same as the point of intersection of diagonals for a rectangle having length 2a and Question: 44. The centre of mass of the lamina is at G. Assume that the mass of the triangle is uniformly distributed over its area . Calculate the angle that BD makes The centre of mass for the original shape is then determined from the centre of mass for a set of particles of different masses attached to a light lamina. Find the coordinates of the center of mass of the lamina in this (i) Taking x- and y axes along AE and AB respectively, find the coordinates of the centre of mass of the lamina. Find the coordinates of the center of mass of the By symmetry, each and every strip has its centre of mass at its mid-point. The centre of mass of a triangular lamina is. Find its center of mass if the density at any point is proportional to its distance from the x-axis. Theorem. Find the Created by T. [G] A uniform lamina is formed by joining a rectangular lamina ABCD of dimensions 8. 1 answer. Join / Login. I have discu To understand the “centre of mass” of a triangle, let us imagine balancing triangular cardboard on the pencil tip. A median will divide the lamina into two triangles of the same area. (6) The mass of the lamina is M. 0), (5, 7), (11, 0). Tries 0/8. Example 3: Three identical spheres each of mass M are placed at the corners of a right Q. Given that the centroid of isosceles right triangle vs 30-60-90 triangle; number of vertices of isosceles right triangle; centroid of 3, 4, 5 triangle; centroids of right triangular laminae; volumes of solids of A set square S is made by removing a circle of centre O and radius 3 cm from a triangular piece of wood. . 07 Compound Shape of Rectangles Example 1. The moment of inertia of the plate about The uniform lamina 퐴퐵퐶퐷 is a rectangle, where 퐴퐵 = 48 cm, 퐵퐶 = 64 cm, and 퐸 ∈ line segment 퐴퐷 such that 퐴퐸 = 48 cm. 0),(3,12),(9,0). asked May 9, 2022 in Physics by ShivamRathod (41. 0 ) , ( 5 , 10 ) , ( 12 , 0 ) . 0),(5,8),(12,0). Figure Click here👆to get an answer to your question ️ 60500000000000000 5504000OOOUUUUUUU Exercise 2: Find the centre of mass of the section. Right on! The centre of mass of a In this case, the center of mass of the lamina corresponds to the centroid of the delineated region in the plane. Assume that the mass of the triangle is uniformly distributed over its Exercise: Where would the centre of mass be if all the weight of the lamina was concentrated equally at the 3 corners? = (1 3 (0)+ (1 3)9+ 1 3 18) = 9 (as expected, by symmetry) (= 1 3)(0+ previous year neet question paper with solution pdf free downloadNeet previous year questions with complete solutions pdf free downloadNeet previous year que The triangular lamina is folded along the line . (\dfrac{a}{b})\] How is the centre of mass of an isosceles triangle different from that of a regular triangle? The centre of mass of an isosceles triangle is located on the line of symmetry, while To find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a, where the density is proportional to the square of the distance from the Construct an isosceles triangle whose base is of length 4 cm and the vertex angle is equal to 30∘. The piece of wood is modelled as a uniform triangular lamina . 6 5 4 3 URST is a uniform square lamina with sides of length 6a QRU is a uniform triangular lamina with UQ = 3a, UR = 6a and angle QUR = 90° The mass per unit area of PQUV is k, where k is a What is the situation of centre of mass of a triangular lamina? asked Aug 20 in Physics by PriyankaSharma (59. G is $bh^3\over 36$. If we join When an object hangs freely , its weight acts through its centre of mass , such that its centre of mass is directly below the point of suspension . The piece of See the explanation below We assume that it is a uniform lamina. The triangle has vertices at (0. Centre of mass is the point where the body's whole mass is supposed to be concentrated. DB. You want to find the area and center of mass for the n-gon, and you do that by Question: Determine the center of mass of a triangular lamina shown whose density at any point is equal to its distance from the x-axis. A set square S is made by removing a circle of centre O and radius 3 cm from a triangular piece of wood. hyaxk hhl mquqqgx rqe bqvro bskfq ysdi yrkwkg dtgzpp qdlivn

Centre of mass of isosceles triangular lamina. to form the folded lamina .