Question

An umbrella is made by stitching $12$ triangular pieces of cloth. Each piece measures $50cm,20cm$ and $50cm$, Find the area of the cloth used in it.

Answer 1

Each area(△) can be calculated by Heron’s Formula, where

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

and semi Perimeter, $\left(s\right)$ $=\frac{a+b+c}{2}$

$=\frac{50+20+50}{2}=\frac{120}{2}=60cm$

Using Heron’s formula,

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

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

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

$=\sqrt{20\times 3\times 10\times 20\times 2\times 10}$

$=20\times 10\sqrt{3\times 2}$

$=200\sqrt{6}c{m}^2$

Area of the $12$ triangular pieces of cloth to make umbrella $=12\times 200\sqrt{6}c{m}^2$

Hence, the total area of the cloth used to make umbrella$=2400\sqrt{6}c{m}^2$