How much paper of each shade is needed to make a kite given in Fig, in

1.	How much paper of each shade is needed to make a kite given in Fig, in which ABCD is a square with diagonal 44 cm.
Answer» According to the figure, AC = BD = 44cm AO = 44/2 = 22cm BO = 44/2 = 22cm From ΔAOB, AB² = AO² + BO² ⇒ AB² = 22² + 22² ⇒ AB² = 2 × 22² ⇒ AB = 22√ 2 cm Area of square = (Side)² = (22√2)² = 968 cm² Area of each triangle (I, II, III, IV) = Area of square /4 = 968 /4 = 242 cm² To find area of lower triangle, Let a = 28, b = 28, c = 14 s = (a + b + c)/2 ⇒ s = (28 + 28 + 14)/2 = 70/2 = 35. Area of the triangle = √s(s-a)(s-b)(s-c) = √35(35-28)(35-28)(35-14) = √35×7×7×21 = 49√15 = 189.77 cm² Therefore, We get, Area of Red = Area of IV = 242 cm² Area of Yellow = Area of I + Area of II = 242 + 242 = 484 cm² Area of Green = Area of III + Area of lower triangle = 242 + 189.77 = 431.77 cm²

How much paper of each shade is needed to make a kite given in Fig, in which ABCD is a square with diagonal 44 cm.

Answer»

According to the figure,

AC = BD = 44cm

AO = 44/2 = 22cm

BO = 44/2 = 22cm

From ΔAOB,

AB² = AO² + BO²

⇒ AB² = 22² + 22²

⇒ AB² = 2 × 22²

⇒ AB = 22√ 2 cm

Area of square = (Side)²

= (22√2)²

= 968 cm²

Area of each triangle (I, II, III, IV) = Area of square /4

= 968 /4

= 242 cm²

To find area of lower triangle,

Let a = 28, b = 28, c = 14

s = (a + b + c)/2

⇒ s = (28 + 28 + 14)/2 = 70/2 = 35.

Area of the triangle = √s(s-a)(s-b)(s-c)

= √35(35-28)(35-28)(35-14)

= √35×7×7×21

= 49√15 = 189.77 cm²

Therefore,

We get,

Area of Red = Area of IV

= 242 cm²

Area of Yellow = Area of I + Area of II

= 242 + 242

= 484 cm²

Area of Green = Area of III + Area of lower triangle

= 242 + 189.77

= 431.77 cm²