Question

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

Answer 1

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 the sheet $=2\times (5\times 96)=₹960$