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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?

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?

            kite

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From the figure:

kite 2

Calculation of the area for each shade:

The shade I:  Triangle ABD

Here, base BD = 32\ cm and the height AO = 16\ cm.

Therefore, the area of triangle ABD will be:

= \frac{1}{2} \times base\times height = \frac{1}{2}\times 32\times 16

= 256\ cm^2

Hence, the area of paper used in shade I is 256\ cm^2.

Shade II: Triangle CBD

Here, base BD = 32\ cm  and height CO = 16\ cm.

Therefore, the area of triangle CBD will be:

= \frac{1}{2} \times base\times height = \frac{1}{2}\times 32\times 16

= 256\ cm^2

Hence, the area of paper used in shade II is 256\ cm^2.

Shade III: Triangle CEF

Here, the sides are of lengths, a = 6\ cm,\ b = 6\ cm\ and\ c = 8\ cm.

So, the semi-perimeter of the triangle:

s = \frac{a+b+c}{2} = \frac{6+6+8}{2} = \frac{20}{2} = 10\ cm.

Therefore, the area of the triangle can be found by using Heron's formula:

Area = \sqrt{s(s-a)(s-b)(s-c)}

            = \sqrt{10(10-6)(10-6)(10-8)}

            = \sqrt{10(4)(6)(2)}

            = 8\sqrt{5}\ cm^2

Hence, the area of the paper used in shade III is 8\sqrt{5}\ cm^2.

 

 

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