Question

How do I find the area of this figure
Pls help

Answer 1

36.5255 cm²

Explanation:

Examining the figure we can see 3 figures and by symmetry these are
2 semicircles and a trapezoid

Area of a semicircle = 1/2 area of circle
Area of circle of diameter d = πr² where r is the radius
r = d/2

so area of semicircle of diameter r = 1/2 π r²

The top semicircle has diameter = 4 cm, radius r = 2 cm

The top semicircle has diameter = 7 cm , radius = 7/2 cm

Area of top semicircle =1/2 x π x 2²
= 1/2 x π x 4
= 2π cm²
= 6.2832 cm²

Area of bottom semicircle = 1/2 x π x (7/2)²
= 1/2 x π x 49/4
= 49/8 π
= 19.2423 cm²

Area of both semicircles = 6.28318 + 19.24225
= 25.5255 cm²

Area of the trapezoid is given by

`(a + b)/(2)h`

where
a and b are the two bases(the parallel sides) and h is the vertical distance between them

In the trapezoid segment we see
a = 4, b = 7 and h = 2

Therefore area of trapezoid segment =
`(4 + 7)/(2) \cdot 2 = 11 \;cm^2`

Area of the composite figure
= 25.5255 + 11
= 36.5255 cm²