A kite is 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 Fig.

How much paper of each side has been used in it ?

Options

A. `8 sqrt5 cm^2`
B. `8 sqrt2 cm^2`
C. `7 sqrt5 cm^2`
D. `7 sqrt2 cm^2`

Answer

A

Explanation

ar(1) = ar(2) = 1/2a(square) `= 512/2 = 256 cm^2`

diagonal `= sqrt2*`side

side = `32/sqrt2`

area(square) =`(32/sqrt2)^2 = 512 cm^2`

`s = (a+b+c)/2 = (6+6+8)/2 = 10cm`

Heron`'`s formula for ar(3) `= sqrt(s(s-a)(s-b)(s-c))`

`= sqrt(10(10-6)(10-6)(10-8))`

`= sqrt(2*5*4*4*2)`

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