Question

Question 6
An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see the given figure), each piece measuring 20cm, 50cm and 50cm.How much cloth of each colour is required for the umbrella?

Answer 1

For each triangular piece,
Semi-perimeter, $s=\frac{(20+50+50)}{2}=60cm$

By Heron’s formula,
Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

Area of each triangular piece
= $\lfloor \sqrt{60(60-50)(60-50)(60-20)}\rfloor c{m}^2=\lfloor \sqrt{60\left(10\right)\left(10\right)\left(40\right)}\rfloor c{m}^2=200\sqrt{6}c{m}^2$

Since there are 5 triangular pieces are made of two different coloured cloths,

Area of each cloth required
= $(5\times 200\sqrt{6})c{m}^2=1000\sqrt{6}c{m}^2$