A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown in Fig. 12.28. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each type of paper needed to make the hand fan.
Answers
Given : The dimensions of equal strips of a hand fan are 25 cm, 25 cm and 14 cm.
Sides of 1 triangular strip of paper are of length a = 25 cm, b = 25 cm, c = 14 cm.
Semi perimeter of Δ (s) = (a + b + c)/2
s = (a + b + c)/2
s = (25 + 25 + 14)/2
s = 64/2
s = 32 cm
By using Heron's formula :
Area of 1 triangular strip , A = s√(s − a)(s − b)(s − c)
A = √32(32 - 25) (32 - 25) (32 - 14)
A = √32 × 7 × 7 × 18
A = √(16 × 2) × 7 × 7 × (9 × 2)
A = √(16) × (7 × 7) × (9) × (2 × 2)
A = 4 × 7 × 3 × 2
A = 28 × 6
A = 168 cm²
Area of 1 triangular strip = 168 m².
Area of each type of paper needed to make the hand fan = 5 × 168 m² = 840 m²
[Each colour paper = 5]
Hence, the area of each type of paper needed to make the hand fan is 840 m².
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