Radha made a picture of an aeroplane with coloured paper as shown in Fig 12.15. Find the total area of the paper used.
Solution:
Length of the sides of the triangle section I = 5cm, 1cm and 5cm
Perimeter of the triangle = 5 + 5 + 1 = 11cm
Semi perimeter = 11/2 cm = 5.5cm
Using heron's formula,
Area of section I = √s (s-a) (s-b) (s-c)
= √5.5(5.5 - 5) (5.5 - 5) (5.5 - 1) cm2
= √5.5 × 0.5 × 0.5 × 4.5 cm2
= 0.75√11 cm2 = 0.75 × 3.317cm2 = 2.488cm2 (approx)
Length of the sides of the rectangle of section I = 6.5cm and 1cm
Area of section II = 6.5 × 1 cm2 = 6.5 cm2
Section III is an isosceles trapezium which is divided into 3 equilateral of side 1cm each.
Area of the trapezium = 3 × √3/4 × 12 cm2 = 1.3 cm2 (approx)
Section IV and V are 2 congruent right angled triangles with base 6cm and height 1.5cm
Area of region IV and V = 2 × 1/2 × 6 × 1.5cm2 = 9cm2
Total area of the paper used = (2.488 + 6.5 + 1.3 + 9)cm2 = 19.3 cm2
