Q7. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Figure How much paper of each shade has been used in it?
From the figure:
Calculation of the area for each shade:
The shade I: Triangle ABD
Here, base and the height
Therefore, the area of triangle ABD will be:
Hence, the area of paper used in shade I is
Shade II: Triangle CBD
Here, base and height
Therefore, the area of triangle CBD will be:
Hence, the area of paper used in shade II is
Shade III: Triangle CEF
Here, the sides are of lengths,
So, the semi-perimeter of the triangle:
Therefore, the area of the triangle can be found by using Heron's formula:
Hence, the area of the paper used in shade III is .