Question

An umbrella is made by stitching 12
triangular pieces of cloth, each measuring
(50 cm x 20 cm x 50 cm). Find the area of
the cloth used in it.
​

Answer 1

Answer:

The sides of triangular pieces are 20 cm, 50 cm and 50 cm.

Let a = 20 cm, b = 50 cm, c = 50 cm

∴ Semi - perimeter, s = (a + b + c)/2 = (20 + 50 + 50)/2

s = 60 cm

∴ Area of one triangular piece = root under (√s(s - a)(s - b)(s - c))

= root under (√60(60 - 20)(60 - 50)(60 - 50))

= root under (√60 x 40 x 10 x 10) = 200√6 cm2

Cloth of each design required = Area of 5 triangular pieces

= 5 x 200√6 = 1000√6 cm2

Answer 2

Given: An umbrella is made up by stitching 12 triangular pieces of cloth, each measuring 50cm,×20cm×50cm.

( √6=2.45 )

To find: Area of the cloth used in it.

Solution:

S = 50+20+50/2

= 120/2

= 60 cm

Area = √{60 (60-50) (60-20) (60-50)}

= √(60×10×40×10)

= √(20×3×10×20×2×10)

= 20×10 √(3×2)

= 200 √6

= 200 × 2.45 [since, √6=2.45]

= 490 cm²

Area of the cloth used in the umbrella

= (490×12) cm²

= 5880 cm²