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 cm². Find the cost of painting.

• A. ₹960
• B. ₹480
• C. ₹300
• D. ₹192

Answer 1

The correct option is A ₹960

All sides of a rhombus are equal
Therefore, AB = BD = DC = CA = 10 cm
Diagonal = 12 cm.
Since the diagonals bisect each other, BO = OC = 6 cm.
Now in $△$AOC, AC = 10 cm, OC = 6 cm and $\angle$AOC = 90°.
Using Pythagoras theorem,
$A{C}^2=A{O}^2+O{C}^2$
$A{O}^2=A{C}^2–O{C}^2=(10{)}^2–(6{)}^2=100-36=64=(8{)}^2$
Therefore, AO = 8 cm
Area of $△$ AOC = $\frac{1}{2}$$\times$base$\times$height = $\frac{1}{2}$ $\times$(OC)$\times$(AO)
Area = $\frac{1}{2}$$\times$6$\times$8 = $24c{m}^2$
Area of the rhombus to be painted = 4 $\times$ Area of $△$AOC
Area of painted rhombus = 4$\times$24 cm² = 96 $c{m}^2$
Cost of painting per $c{m}^2$ = ₹5
Cost of painting of one side of the rhombus = ₹5$\times$96 = ₹480
Cost of painting of both side of the rhombus = 2$\times$₹480 = ₹960