A semicircle has been drawn on the length of a rectangle. The area of the shaded region in the figure is: 
To find the area of the shaded region, we first determine the areas of the rectangle and the semicircle, then subtract the area of the semicircle from the area of the rectangle.
- Calculate the area of the rectangle:
The rectangle's length is 14 cm, and its width is 10 cm.
Area of rectangle = \(14 \, \text{cm} \times 10 \, \text{cm} = 140 \, \text{cm}^2\)
- Calculate the area of the semicircle:
The diameter of the semicircle is equal to the length of the rectangle, which is 14 cm. Therefore, the radius is half of the diameter.
Radius = \(\frac{14}{2} = 7 \, \text{cm}\)
Area of semicircle = \(\frac{1}{2} \pi r^2 = \frac{1}{2} \times \frac{22}{7} \times 7^2 = 77 \, \text{cm}^2\)
- Find the area of the shaded region:
Area of shaded region = Area of rectangle - Area of semicircle
= \(140 \, \text{cm}^2 - 77 \, \text{cm}^2 = 63 \, \text{cm}^2\)
Thus, the area of the shaded region is 63 cm².
Similar Questions
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- Find the perimeter of a semicircle with a radius of 7 cm. (Use $\pi = \frac{22}{7}$)
- What is the area of a rhombus, whose sides are 25 cm and one of the diagonals is 14 cm?
- A sector of a circle has a radius of $18\text{ cm}$ and a central angle of $125^\circ$. What will be its approximate perimeter?
(Use $\pi = \frac{22}{7}$) - Area of a square is equal to ten times the area of a rectangle of edge 5 cm $\times$ 8 cm. What is the perimeter of the square?
- If the length and the perimeter of a rectangle are in the ratio of 3 : 20, then its length and breadth will be in the ratio of:
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Important Questions from 2-D Mensuration
- The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field? Take $\pi = \frac{22}{7}$
- Find the area of a sector with a central angle of 150° in a circle with a radius of 12 cm.
- The area of a square is $2304$ cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
- The length of a rectangular pitch is 30 m more than its breadth. Its area is $18,271$ m$^{2}$. Its breadth (in m) is:
