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In given figure, ABCD is a rectangle. The radius of the semicircles drawn on AD and BC as diameters and radius of circle drawn in between is the same. If BC=7cm, find the area of the shaded region?
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In given figure, ABCD is a rectangle. The radius of the semicircles dr...
Given:
- ABCD is a rectangle
- The radius of the semicircles drawn on AD and BC as diameters is the same
- The radius of the circle drawn in between is also the same as the radius of the semicircles
- BC = 7 cm

To find:
The area of the shaded region

Explanation:

Step 1: Find the radius of the semicircles and the circle
Since the radius of the semicircles and the circle are the same, we only need to find the radius once.

To find the radius, we can use the length of BC, which is given as 7 cm. Since BC is the diameter of one of the semicircles, the radius will be half of BC.

Radius of the semicircles = BC/2 = 7/2 = 3.5 cm

Step 2: Find the area of the semicircles
The area of a semicircle is half the area of a full circle with the same radius.

Area of one semicircle = (1/2) * π * r^2
= (1/2) * 3.14 * (3.5)^2
= (1/2) * 3.14 * 12.25
= 19.185 cm^2

Since there are two semicircles, the total area of the semicircles is 2 times the area of one semicircle.

Total area of the semicircles = 2 * 19.185 cm^2
= 38.37 cm^2

Step 3: Find the area of the circle
The area of a circle can be calculated using the formula:

Area of a circle = π * r^2
= 3.14 * (3.5)^2
= 3.14 * 12.25
= 38.465 cm^2

Step 4: Find the area of the shaded region
The shaded region is the difference between the area of the semicircles and the area of the circle.

Area of shaded region = Total area of the semicircles - Area of the circle
= 38.37 cm^2 - 38.465 cm^2
= -0.095 cm^2

Answer:
The area of the shaded region is -0.095 cm^2.
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In given figure, ABCD is a rectangle. The radius of the semicircles dr...
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In given figure, ABCD is a rectangle. The radius of the semicircles drawn on AD and BC as diameters and radius of circle drawn in between is the same. If BC=7cm, find the area of the shaded region?
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