Question

A kite in the shape of a square with a diagonal 32 cm and an isosceles triangles of base 8 cm and sides 6 cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it ?

Answer 1

We know that the diagonals of a square are perpendicular bisectors of each other.
Given diagonal BD = AC = 32 cm, OA $\frac{1}{2}$AC = 16 cm.
So square ABCD is divided into two isosceles triangles ABD and CBD of base 32 cm and height 16 cm.
Area of ∆ABD = $\frac{1}{2}$ × base × height = 256 cm²
Since the diagonal divides the square into two equal triangles. Therefore, Area of ∆ABD = Area of ∆CBD = 256 cm²
Now, for ∆CEF
Semi Perimeter(s) = $\frac{a+b+c}{2}$= 10 cm
Area of ∆CEF = $\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{10(10-6)(10-6)(10-8)}=\sqrt{10\times 4\times 4\times 2}=8\sqrt{5}=8\times 2.24=17.92c{m}^2$
Thus, the area of the paper used to make region I = 256 cm², region II = 256 cm², and region III = 17.92 cm².