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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?

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#### Solution

We know that

Area of square = 1/2(diagonal)^{2}

`"Area of the given kite "= 1/2(32 cm)^2 = 512 cm^2`

Area of 1^{st} shade = Area of 2^{nd} shade = 512/2 = 256 cm^{2}

Therefore, the area of paper required in each shape is 256 cm^{2}.

**For III**^{rd}** triangle**

Semi-perimeter,

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

By Heron’s formula,

`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`

`"Area of 3rd triangle "=sqrt(10(10-6)(10-6)(10-8))`

`=(sqrt(10xx4xx4xx2))cm^2`

`=(4xx2sqrt5)cm^2`

`=8sqrt5 cm^2`

= (8 x 2.24) cm^{2}

= 17.92 cm^{2}

Area of paper required for III^{rd} shade = 17.92 cm^{2}

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