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Question -

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 the figure. How much paper of each shade has been used in it?
                                     



Answer -

   

Let the kite is made square ABCD and an isosceles ADEF.
Given, sides of ADEF are DE = DF = 6 cm and EF = 8 cm.
Also, diagonal of square ABCD = 32 cm
We know that diagonals of a square bisect each other at right angle.
OA = OB = OC = OD = = 16 cm
Now, area of region I = 2 x Area of AAOB = 2 x  x OA x OB
[∵ area of right angled triangle =  x base x height]

Hence, the area of paper of I color used in making kite = 256 cm2 Area of paper of II color used in making kite = 256 cm2 and area of paper of III color used in making kite = 17.92 cm2
 

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