An Umbrella Is Made By Stitching 12 Triangular Pieces Of Cloth. Each Piece Measures 50Cm, 20Cm And 50Cm, Find The Area Of The Cloth Used In It.

Given, an umbrella is made of 12 triangular pieces each measuring 50 cm, 20 cm, 50 cm.

The area of cloth required is

Semi perimeter, s = \( \frac{sum of sides of triangle}{2} \)

= \( \frac{50 + 20 + 50}{2} \)

= 60 cm

Using heron’s formula, Area of one triangular piece = \( \sqrt{s (s – a)(s – b)(s – c)} \)

= \( \sqrt{60 * 10 * 40 * 10} \)

= \( \sqrt{60 * 10 * 40 * 10} \)

= \( 200\sqrt{6}cm^{2} \)

Area of 12 triangular pieces or area of cloth used = Area of one triangular piece * 12

= \( 200\sqrt{6}cm^{2} * 12 \)

= \( 2400\sqrt{6}cm^{2} \)

Therefore, the area of cloth required is \( 2400\sqrt{6}cm^{2} \)

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