Calculate the area of the shaded region, if the diameter of the semi-circle is 14 cm.

Given,

Diameter of semicircle = 14 cm

radius = $\dfrac{14}{2}$ = 7 cm

Calculating the area of semi-circle EDF,

$\text{Area of semi-circle EDF} = \dfrac{1}{2} \times πr^2 \\[1em] = \dfrac{1}{2} \times \dfrac{22}{7} \times 7^2 \\[1em] = \dfrac{11}{7} \times 49 \\[1em] = 11 \times 7 \\[1em] = 77 \text{ cm}^2.$

From figure,

AC = ED = 14 cm

Since, AB = BC

Thus, AB = BC = $\dfrac{AC}{2} = \dfrac{14}{2}$ = 7 cm.

From figure,

AE = AB = 7 cm.

Area of rectangle ACDE = AC × AE

= 14 × 7 = 98 cm².

ABE and BCD are two quadrants each with radius 7 cm.

Calculating the area of two quadrants,

$\text{Area of two quadrants} = 2 \times \dfrac{1}{4}πr^2 \\[1em] = \dfrac{1}{2} \times \dfrac{22}{7} \times 7^2 \\[1em] = \dfrac{11}{7} \times 49 \\[1em] = 11 \times 7 \\[1em] = 77 \text{ cm}^2.$

Area of shaded region = Area of semi-circle EDF + Area of rectangle ACDE - Area of two quadrants

= 77 + 98 - 77 = 98 cm².

Hence, area of shaded region = 98 cm².