Question

A rhombus-shaped sheet with a perimeter of 40cm and one diagonal of 12cm, is painted on both sides at the rate of ₹ 5 per $c{m}^2$. Find the cost of painting.

• A. ₹ 480
• B. ₹ 940
• C. ₹ 490
• D. ₹ 960

Answer 1

The correct option is D

₹ 960

Perimeter of Rhombus $=40cm$

$\Rightarrow 4\times \text{side}=40cm$

$\Rightarrow \text{side}=10cm$

One diagonal $=12cm$. As rhombus is also a parallelogram, so its diagonals divide it into two congruent triangles of equal area. Area of rhombus = 2(Area of triangle with sides 10cm, 10cm and 12 cm)

$S=\frac{10+10+12}{2}=16$

Area of triangle

$=\sqrt{16(16-10)(16-10)(16-12)}$

$=\sqrt{16\times 6\times 6\times 4}$

$=4\times 6\times 2=48c{m}^2$

$\therefore$ Area of Rhombus $=2\times 48=96c{m}^2$

Cost of painting $=2\times (5\times 96)=₹960$