Question

An umbrella is made by stitching $ 10$ triangular pieces of cloth of two different colors (see Fig.12.16), each piece measuring $ 20 cm, 50 cm$ and $ 50 cm$. How much cloth of each color is required for the umbrella?

Answer 1

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

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

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

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

Using Heron’s formula,

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

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

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

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

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

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

Hence, the total area of the cloth of each color $=5\times 200\sqrt{6}c{m}^2$

$=1000\sqrt{6}c{m}^2$