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 m2. Find the cost of painting.
In a rhombus, all sides are equal.
Perimeter of rhombus = 40cm
Side of rhombus = 40/4 = 10cm
a = 10, b = 10, c = 12
s = (a + b + c)/2
⇒ s = (10 + 10 + 12)/2 = 32/2 = 16.
Area(ΔBCD) = √s(s-a)(s-b)(s-c)
⇒ Area(ΔBCD) = √16(16-10)(16-10)(16-12)
⇒ Area(ΔBCD) = √16×6×6×4
⇒ Area(ΔBCD) = 48 cm2
As ABCD is a rhombus, Area(ΔBCD) = Area(ΔABD)
⇒ Area of rhombus(ABCD) = Area(ΔBCD) + Area(ΔABD)
⇒ Area of rhombus(ABCD) = 48 + 48
⇒ Area of rhombus(ABCD) = 96cm2