A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is

1.	A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.
Answer» In a rhombus, all sides are equal. Perimeter of rhombus = 40 cm Side of rhombus = 40/4 = 10 cm a = 10, b = 10, c = 12 s = (a + b + c)/2 ⇒ s = (10 + 10 + 12)/2 = 32/2 = 16. Area(ΔBCD) = √s(s-a)(s-b)(s-c) ⇒ Area(ΔBCD) = √16(16-10)(16-10)(16-12) ⇒ Area(ΔBCD) = √16×6×6×4 ⇒ Area(ΔBCD) = 48 cm² As ABCD is a rhombus, Area(ΔBCD) = Area(ΔABD) ⇒ Area of rhombus(ABCD) = Area(ΔBCD) + Area(ΔABD) ⇒ Area of rhombus(ABCD) = 48 + 48 ⇒ Area of rhombus(ABCD) = 96cm²

A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.

Answer»

In a rhombus, all sides are equal.

Perimeter of rhombus = 40 cm

Side of rhombus = 40/4 = 10 cm

a = 10, b = 10, c = 12

s = (a + b + c)/2

⇒ s = (10 + 10 + 12)/2 = 32/2 = 16.

Area(ΔBCD) = √s(s-a)(s-b)(s-c)

⇒ Area(ΔBCD) = √16(16-10)(16-10)(16-12)

⇒ Area(ΔBCD) = √16×6×6×4

⇒ Area(ΔBCD) = 48 cm²

As ABCD is a rhombus, Area(ΔBCD) = Area(ΔABD)

⇒ Area of rhombus(ABCD) = Area(ΔBCD) + Area(ΔABD)

⇒ Area of rhombus(ABCD) = 48 + 48

⇒ Area of rhombus(ABCD) = 96cm²