Question

An umbrella is to be made using 8 triangular pieces of cloth measuring 13 cm, 13 cm, and 10 cm each.
Find the area of the cloth required for making the umbrella.

Answer 1

8 isosceles triangles of sides $13cm,13cm,10cm$

By Heron's Formula,

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

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

$s=\frac{13+13+10}{2}=18$

Area of triangle $=\sqrt{18\times (18-13)\times (18-13)\times (18-10)}$ (Heron's formula)

Area of triangle $=\sqrt{18\times 5\times 5\times 8}$

$=5\sqrt{144}$

Area of triangle $=60c{m}^2$

Area of cloth made of 8 triangles $=60\times 8$

$=480c{m}^2$