Question

An umbrella is made by stitching $10$ triangular pieces of cloth of $5$ different colour each piece measuring $20$cm, $50$cm and $50$cm. How much cloth of each colour is required for one umbrella?

Answer 1

Area of each cloth $=5\times$ (Area of a triangle)

Area of triangle $=\sqrt{S(S-a)(S-b)(S-c)}$

$a=50cm$

$b=20cm$

$c=50cm$

$S$ = semi perimeter

$a,b,c=$ sides of triangle

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

Area of triangle $=\sqrt{60(60-50)(60-20)(60-50)}$

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

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

Area of triangle / umbrella $=5\times 200\sqrt{6}c{m}^2=1000\sqrt{6}$