An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see Fig.12.16), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?
Solution
Semi perimeter of each triangular piece = (50 + 50 + 20)/2 cm = 120/2 cm = 60cm
Using heron's formula,
Area of the triangular piece = √s (s-a) (s-b) (s-c)
= √60(60 - 50) (60 - 50) (60 - 20) cm2
= √60 × 10 × 10 × 40 cm2
= 200√6 cm2
Area of triangular piece = 5 × 200√6 cm2 = 1000√6 cm2
