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?
[4 MARKS]
Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks
For each triangular piece,
Semi-perimeter, s = (20+50+50)2 = 60cm
By Heron’s formula,
Area of triangle = √s(s−a)(s−b)(s−c)
Area of each triangular piece = ⌊√60(60−50)(60−50)(60−20)⌋cm2=⌊√60(10)(10)(40)⌋cm2=200√6cm2
Since there are 5 triangular pieces are made of two different coloured cloths,
Area of each cloth required = (5×200√6)cm2=1000√6cm2