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A kite in the shape of a square with each diagonal 32 cm and having a tail in the shape of an isosceles triangle of base 8 cm and each side 6 cm, is made of three different shades as shown in the figure. The total area of paper used in it is:

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510 c m 2

530 c m 2

560 c m 2

590 c m 2

answer is B.

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Detailed Solution

Given diagonal is 32 cm for the square.
Base of isosceles triangle=8cm
Side of isosceles triangle=6cm
As, the diagonal of a square is equal to

a 2

where a is the side.

⇒ a 2 = 32 ⇒ a 2 = 25 ⇒ a = 2 5 − 1 / 2 ⇒ a = 162 c m

Now, the area is,

A r e a of square = a 2 ⇒ A r e a of square = (162) 2 ⇒ A r e a of square = 512 c m 2

Now, as square ABCD is divided into 2 triangle of equal area,
Therefore, the area of triangle ABD and BCD is,

⇒ A r e a of triangle ABD and BCD = 5122

⇒ A r e a of triangle ABD and BCD = 256 c m 2

Now, the area of tail is calculated using Heron’s formula,
a = 8 cm
b = 6 cm
c = 6 cm
Semi-perimeter(s) is calculated as,

s = a + b + c 2 ⇒ s = 8 + 6 + 6 2 ⇒ s = 2010 ⇒ s = 10 c m

Now, area by Heron’s formula is given by,

A = s (s − a) (s − b) (s − c) ⇒ A = 10 (10 − 8) (10 − 6) (10 − 6) ⇒ A = 10 × 2 × 4 × 4 ⇒ A = 85

⇒ A = 8 × 2.24 ⇒ A = 17.92 c m 2

The total area is,

A r e a = 216 + 216 + 17.92 ⇒ A r e a = 529.92 c m 2 ⇒ A r e a ≃ 530 c m 2

The total area is

.
Hence, option 2 is correct.

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