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

Answer:

Area of the shaded region be 251.74 cm² .

Step-by-step explanation:

Formula

$Area\ of\ trapezoid = \frac{1}{2}\times sum\ of\ parallel\ sides\times height$

i.e

$Area\ of\ trapezoid = \frac{1}{2}\times (AB+DC)\times h$

As shown in the figure.

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

Putting in the above

$Area\ of\ trapezoid = \frac{1}{2}\times (28+12)\times 14$

$Area\ of\ trapezoid = \frac{1}{2}\times 40\times 14$

$Area\ of\ trapezoid = \frac{1\times 560}{2}$

Area of trapezoid = 280 cm²

Formula

$Area\ of\ semicircle = \frac{1}{2}\ \pi r^{2}$

Where r is the radius of the circle.

$r = \frac{DC}{4}$

$r = \frac{12}{4}$

r = 3 cm

$\pi = 3.14$

$Area\ of\ two\ semicircle = \frac{2}{2}\times 3.14\times 3\times 3$

$Area\ of\ two\ semicircle = 3.14\times 3\times 3$

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 .