Question

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

• A. Rs. $960$
• B. Rs. $2400$
• C. Rs. $1200$
• D. Rs. $480$

Answer 1

The correct option is A Rs. $960$

Given, Perimeter of rhombus $=40cm$

All sides of rhombus are equal, hence, side, $a=\frac{40}{4}=10cm$

Diagonal of rhombus, $p=12cm$
Area of rhombus $=\frac{1}{2}p\sqrt{4a^2-p^2}$
Area of rhombus $=\frac{1}{2}\left(12\right)\sqrt{4(10{)}^2-{12}^2}$

Area of rhombus $=96$ $c{m}^2$
Total area of both the sides $=2\times 96=192c{m}^2$
Cost of painting $1c{m}^2$ = Rs. $5$
Cost of painting $192c{m}^2=192\times 5=$ Rs. $960$