Question

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours each piece measuring 20 cm,50 cm and 50 cm. How much cloth of each colour is required for umbrella?

Answer 1

Area of triangle by heron's formula

semi-perimeter is given by

$s=\frac{a+b+c}{2}$

$=\frac{20+50+50}{2}=60$

$\sqrt{s(s-a)(s-b)(s-c)}$

Area of each piece of cloth =$\sqrt{\left(60\right)(60-20)(60-50)(60-50)}$

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

=$\sqrt{240000}$

=$\sqrt{24}\times 100$

=$489.8979{cm}^2$

Total cloth required =$10\times 489.8979{cm}^2=4898.979{cm}^2$

Area of cloth of each color required is

$\frac{4898.979}{2}{cm}^2=2449.489{cm}^2$