A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per cm2. Find the cost of painting.
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 ∠AOC = 90°.
Using Pythagoras theorem,
AC2=AO2+OC2
AO2=AC2–OC2=(10)2–(6)2=100−36=64=(8)2
Therefore, AO = 8 cm
Area of △ AOC = 12×base×height = 12 ×(OC)×(AO)
Area = 12×6×8 = 24 cm2
Area of the rhombus to be painted = 4 × Area of △AOC
Area of painted rhombus = 4×24 cm2 = 96 cm2
Cost of painting per cm2 = Rs 5
Cost of painting of the entire rhombus = Rs 5×96 = Rs 480