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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?
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Answer :

Since, the kite is in the shape of a square.

Each diagonal of square = 32 cm ...(Given)

We know that, the diagonals of a square bisect each other at right angle.

image

For Part I :
Area of Part I
= 12 × Base × Height
= 12 × 32 × 16
= 16 × 16 = 256cm2

For Part II :
Area of Part II
= 12 × Base × Height
= 12 × 32 × 16
= 16 × 16 = 256cm2

For Part III :
It is a triangle with sides 6 cm, 6 cm and 8 cm.
Now, we know that,

s=a+b+c2
? s=6+6+82=202=10cm

Now, Area of triangle
= 10(10?6)(10?6)(10?8)
(Since, Heron's formula [area = s(s?a)(s?b)(s?c)])
= 10×4×4×2

= 5×2×4×4×2
= 2×45cm2
= 85cm2
= 8 × 2.24 cm = 17.92 cm2

Hence, the area of colour used for Paper I = 256 cm2

The area of colour used for Paper II = 256 cm2

The area of colour used for Paper III = 17.92 cm2