Question

Find the shaded area in the given rectangle: AB = 40 cm, BC = 21 cm.

Answer 1

Given:

• Rectangle ABCD with AB = 40 cm and BC = 21 cm.
• Two semicircles are drawn inside the rectangle on sides AD and BC as diameters.

Step-wise calculation:

1. Length AB = 40 cm   ...(Length of the rectangle)

2. Length BC = 21 cm   ...(Breadth of the rectangle)

3. The semicircles are drawn on sides AD and BC, which means their diameters equal BC = 21 cm since AD = BC as opposite sides in a rectangle.

4. Radius of each semicircle = `"Diameter"/2`

= `21/2`

= 10.5 cm

5. Area of one semicircle = `1/2 xx π xx r^2`

= `1/2 xx 22/7 xx 10.5^2`

= `1/2 xx 22/7 xx 110.25` 

= `1/2 × 346.5`

= 173.25 cm²

6. Total area of two semicircles = 2 × 173.25 = 346.5 cm².

7. Area of the rectangle = AB × BC

= 40 × 21

= 840 cm²

8. The shaded area in the figure is the area of the rectangle minus the areas occupied by the two semicircles on the sides.

9. Shaded area = Area of rectangle – Area of two semicircles

= 840 – 346.5

= 493.5 cm²

The shaded area in the given rectangle is 493.5 cm².