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?

We know that, Heron's formula

Area of triangle = $\sqrt{s (s - a) (s - b) (s -c)}$

where, s is the semi-perimeter = half of the perimeter

and  a, b and c are the sides of the triangle 

a = 50 cm, b = 50 cm, c = 20 cm

Semi Perimeter

s = (a $+$ b $+$ c)/2

= (50$+$ 50 $+$ 20)/2

= 120/2

= 60 cm

By using  above formula,

Area of one triangle = $\sqrt{s (s - a) (s - b) (s -c)}$

= $\sqrt{60(60 - 50)(60 - 50)(60 - 20)}$

= $\sqrt{60 \times 10 \times 10 \times 40}$

= 200$\sqrt{6}$ cm²

Therefore,

Area of 10 triangular pieces = 10 $\times$ 200$\sqrt{6}$cm² 

= 2000$\sqrt{6}$ cm²

Hence, cloth required for each colour = (Total area of the cloth)/2

= (2000$\sqrt{6}$)/2

= 1000$\sqrt{6}$ cm²