Question

An umbrella is made by stitching $6$ triangular pieces of cloth of red and black colours each measuring $20$cm, $50$cm, and $50$cm. How much cloth of each colour is required for umbrella?

Answer 1

Total cloth required per colour $=6\times$ Area of one part

Area of one part :-

sides $\to 20,50,50$

$s=\frac{a+b+c}{2}=\frac{20+50+50}{2}=60$

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

Area $=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{60\left(40\right)\left(10\right)\left(10\right)}=100\sqrt{24}$

Area $=200\sqrt{6}$ sq units

So, Total cloth required per colour $=6\times 200\sqrt{6}=1200\sqrt{6}$ ${unit}^2$