Question

The centre of each semicircle is on DC.

Work out the area of the shaded region.
Give your answer correct to 3 significant figures.

Answer 1

Area of the shaded region be 251.74 cm² .

Explanation:

Formula

`Area\ of\ trapezoid = (1)/(2)* sum\ of\ parallel\ sides* height`

i.e

`Area\ of\ trapezoid = (1)/(2)* (AB+DC)* h`

As shown in the figure.

AB = 28 cm , DC = 12cm and h = 14 cm

Putting in the above

`Area\ of\ trapezoid = (1)/(2)* (28+12)* 14`

`Area\ of\ trapezoid = (1)/(2)* 40* 14`

`Area\ of\ trapezoid = (1* 560)/(2)`

Area of trapezoid = 280 cm²

Formula

`Area\ of\ semicircle = (1)/(2)\ \pi r^(2)`

Where r is the radius of the circle.

`r = (DC)/(4)`

`r = (12)/(4)`

r = 3 cm

`\pi = 3.14`

`Area\ of\ two\ semicircle = (2)/(2)* 3.14* 3* 3`

`Area\ of\ two\ semicircle = 3.14* 3* 3`

Area of two semicircle = 28.26 cm²

Area of the shaded area = Area of trapezoid - Area of two semicircle

= 280 cm² - 28.26 cm²

= 251.74 cm²

Therefore the area of the shaded region be 251.74 cm² .