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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 Fig. 12.17. How much

paper of each shade has been used in it?

Answer:

As the kite is in the shape of a square, its area will be

\begin{array}{l} A=(1 / 2) \times(\text { diagonal })^{2} \\ \Rightarrow \text { Area of the kite }=(3 / 2) \times 32 \times 32=512 \mathrm{cm}^{2} \end{array}

The area of shade I = Area of shade II

\begin{aligned} &\Rightarrow 512 / 2 \mathrm{cm}^{2}=256 \mathrm{cm}^{2}\\ &\text { So, the total area of the paper that is required in each shade }=256 \mathrm{cm}^{2} \end{aligned}

For the triangle section (III),

The sides are given as 6 cm, 6 cm and 8 cm

Now, the semi perimeter of this isosceles triangle = (6 + 6 + 8)/2 cm = 10 cm

By using Heron's formula, the area of the III triangular piece will be

= √[s (s-a) (s-b) (s-c)]

\begin{array}{l} =\sqrt{10}(10-6)(10-6)(10-8) \mathrm{cm}^{2} \\ =\sqrt{10 \times 4 \times 4 \times 2 \mathrm{cm}^{2}} \\ =8 \mathrm{v} 6 \mathrm{cm}^{2} \end{array}

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