An umbrella is made by stitching 10 triangular pieces of cloth of two different colors (shown in the adjoining figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?

Semi-perimeter (s) = $\dfrac{a + b + c}{2} = \dfrac{20 + 50 + 50}{2} = \dfrac{120}{2}$ = 60 cm.

Total 10 triangular pieces of cloth are required. So, 5 of each colour.

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

Substituting values we get,

$A = \sqrt{60(60 - 20)(60 - 50)(60 - 50)} \\[1em] = \sqrt{60 \times 40 \times 10 \times 10} \\[1em] = \sqrt{240000} \\[1em] = 200\sqrt{6} \text{ cm}^2.$

There are 5 triangular pieces. So area of 5 pieces = $5 \times 200\sqrt{6} = 1000\sqrt{6}$ cm².

Hence, $1000\sqrt{6}$ cm² of each colour cloth is required.