A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10

1.	A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs. 5 per m2. Find the cost of painting.
Answer» Since the sides of a rhombus are equal there fore each side = \(\frac{perimeter}4\) = \(\frac{22}4\) = 8 m Let a, b and c are the sides of triangle and s is the semi-perimeter, then its area is given by: A = \(\sqrt{s(s-a)(s-b)(s-c)}\)where s = \(\frac{a+b+c}2\)[Heron’s Formula] s = \(\frac{a+b+c}2\) = \(\frac{8+8+10}2\) = 13 A = \(\sqrt{13(13-8)(13-8)(13-10)}\) A = \(\sqrt{13\times5\times5\times3}\) = 31.22 cm² Hence, area of rhombus ABCD = 2 ×31.22 m² = 62.44 m² Total painting area of rhombus = 62.44 × 2 = 124.88 m² Cost of painting of rhombus on both sides = 124.88 × 5 = Rs 624.50

A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs. 5 per m2. Find the cost of painting.

Answer»

Since the sides of a rhombus are equal there fore each side = \(\frac{perimeter}4\) = \(\frac{22}4\) = 8 m

Let a, b and c are the sides of triangle and s is

the semi-perimeter, then its area is given by:

A = \(\sqrt{s(s-a)(s-b)(s-c)}\)where s = \(\frac{a+b+c}2\)[Heron’s Formula]

s = \(\frac{a+b+c}2\) = \(\frac{8+8+10}2\) = 13

A = \(\sqrt{13(13-8)(13-8)(13-10)}\)

A = \(\sqrt{13\times5\times5\times3}\) = 31.22 cm²

Hence, area of rhombus ABCD = 2 ×31.22 m²

= 62.44 m²

Total painting area of rhombus = 62.44 × 2 = 124.88 m²

Cost of painting of rhombus on both sides = 124.88 × 5 = Rs 624.50