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Question:

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

Solution:

Here a=50, b=50, c=20
The umbrella's figure consists of 5 triangle pieces
One triangle piece's Area = √s(s-a)(s-b)(s-c) ⇒ 2S = 50 + 50 + 20 ⇒ S = 120/2 = 60 cm
⇒ A = √60(10)(10)(40) = 200√6 cm²
Total Area = 5 × 200√6 = 1000√6 cm²