Question

Find the area of the figure ABCDEFA shown in fig 19.58​

Answer 1

Answer:

(15+2π)cm²

Step-by-step explanation:

Let divide the given figure in 3 parts as:-

1) Half Circle AEF

2) Rectangle ABDE

3) Triangle BCD

We shall now find the area of these 3 parts individually.

1) Area of Half Circle AEF:-

Radius of Circle(r) = 2 cm

Area of Half Circle = πr²/2

                               = (π×2²)/2

                               = 4π/2

                         A₁  = 2π cm²

2) Area of  Rectangle ABDE

Length of Rectangle (l) = 2 + 2 = 4cm

Breadth of Rectangle (b) = 3 cm

Area of Rectangle = l × b

                              = 4 × 3

                        A₂  = 12 cm²

3) Area of Triangle BCD

Base of Triangle(b) = 4 cm

Height if Triangle (h) = 1.5 cm

Area of Triangle = 1/2 × b × h

                           = 1/2 × 4 × 1.5

                           = 2 × 1.5

                      A₃ = 3 cm²

Thus area of figure ABCDEFA = A₁ + A₂ + A₃

                                                    = 2π + 12 + 3

                                                    = (15 + 2π) cm²

Further we can it by putting the value of π = 3.14

15 + 2π = 15 + 2×3.14       

            = 15 + 6.28

            = 21.28 cm²