Question

An umbrella is made by stitching 8 triangular pieces of cloth of two different colours, each piece measures 60cm, 60cm and 20cm. How much cloth of each colour is required for the umbrella?

(a) \(50\sqrt{35} cm^2\)

(b) \(25\sqrt{65} cm^2\)

(c) \(50\sqrt{45} cm^2\)

(d) \(25\sqrt{55} cm^2\)

I have been asked this question in semester exam.

Question is from Application of Heron’s Formula in finding Areas of Quadrilaterals in chapter Heron’s Formula of Mathematics – Class 9

Answer 1

Correct option is (a) \(50\sqrt{35} cm^2\)

The explanation: s = \(\frac{a+b+c}{2}=\frac{60+60+20}{2} = \frac{140}{2}\) = 70

According to heron’s formula, area of the triangle = \(\sqrt{s*(s-a)*(s-b)*(s-c)}\)

= \(\sqrt{70*(70-60)*(70-60)*(70-20)}\)

= \(\sqrt{70*10*10*50}\)

= 100\(\sqrt{35} cm^2\)

This area is the combined area of both colours.

Hence, area of each colour = \(\frac{100\sqrt{35}}{2}\)

= \(50\sqrt{35} cm^2\).