 Hello and welcome to the session. Let us discuss the following question. It says a kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of waist 8 cm and size 6 cm each is to be made of three different shades as shown in figure 12.17. How much paper of each shade has been used in it? So this is the figure 12.17 we need to refer. We need to find the paper of each shade used to make this kite which is in the shape of square plus an isosceles triangle. So let us name this square as A, B, C, D. Let this vertex be E and this is F and the point of intersection of diagonal B O. Also we have given that the length of the diagonal of the square is 32 cm and we know that diagonals of a square bisect each other at right angle. So let us now move on to the solution with all this information. Now area of shade 1, this green shade is equal to area of triangle A O B plus area of triangle A O D. Now we need to find the length of A O, B O and A B. So in triangle A O B we have B O is equal to half of B D. This is because the diagonals bisect each other at right angle. That means half of B D will be 16 cm. So B O will be 1 by 2 into 32 cm that is 16 cm and this is equal to A O. Now area of triangle A O B is equal to 1 by 2 into base into height that is 1 by 2 into base which is 16 cm into height which is also 16 cm. So this is equal to 256 by 2 cm square. Now area of triangle A O B will be same as area of triangle A O B. So in triangle A O D A O is equal to D O which is also equal to B O. So area of triangle A O D is equal to area of triangle A O B which is equal to 256 upon 2 cm square. Now we know that area of shade 1 is area of triangle A O B plus area of triangle A O D. That is the area of triangle A B D. Now we also need to find the area of shade 2 but area of shade 2 will be same as area of shade 1 this is because the diagonals of the square are of the same length that means if B D is 32 cm then A C is also 32 cm and also they bisect. Then the dimension of the triangles C O D and C O B will be same as dimensions of the triangles A O B and A O D. So the area of triangle A B D will be same as area of triangle B C D that is the area of shade 2 and this is equal to 256 cm square. We also need to find the area of this shade 3 which is an isosceles triangle with base 8 cm and each side is 6 cm it's an isosceles triangle. That means area of shade 3 is the area of triangle C E F in triangle C E F. We need to find S to use the Erron's formula. S is 8 plus B plus C by 2 here A is 6 B is 8 and C is 6. So S is 6 plus 8 plus 6 upon 2 and that is equal to 10 and the area of triangle C E F is equal to S minus A into S minus B into S minus C. So this is equal to under the root of 10 into 10 minus 6 into 10 minus 8 into 10 minus 6 which is equal to under the root of 10 into 4 into 2 into 4 which is equal to 4 into root 20 which is equal to 17.92 and since it's the area and the unit of length is given to be centimeter so the unit of area will be centimeter square and this is the area of shade 3. Area of shade 1 is equal to area of shade 2 is equal to 256 centimeter square and area of shade 3 is equal to 17.92 centimeter square. So this completes the question. Hope you enjoyed this session. Goodbye and take care.