Question

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

Answer 1

Here $a=50,b=50,c=20$

The umbrella's figure consists of $5$ triangle pieces

One triangle piece's Area $=\sqrt{s(s-a)(s-b)(s-c)}$

$\Rightarrow 2S=50+50+20$

$\Rightarrow S=\frac{120}{2}=60cm$

$\Rightarrow$$A=\sqrt{60\left(10\right)\left(10\right)\left(40\right)}$

$=200\sqrt{6}{cm}^2$

Total Area $=5\times 200\sqrt{6}=1000\sqrt{6}{cm}^2$