Question

A rectangle is placed around a semicircle as shown below. The width of the rectangle is 5yd. Find the area of the shaded region.

Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

Answer:

10.75 square yards

Step-by-step explanation:

area of a circle is pi x radius squared

radius here is 5

there is only half a circle so divide this answer in 1/2.

area of the rectangle is base x height

10 x 5 = 50 square yards

subtract the are of the circle from the area of the rectangle.

50 - 1/2(25*3.14) = 50 - 39.25 = 10.75

Answer 2

The Area of shaded region will be 15.188 sq. yd

Concept

• First we will the find the area covered by rectangle and the semicircle
• After that to find area of shaded region we will subtract the area of rectangle from area of semicircle

How to solve this problem?

The steps are as follow:

• Given,

For rectangle,

Length of side, L = 5 yd

For semicircle,

Diameter, D = 5 yd

• Formula for area of rectangle is A = L²
• Formula for area of semicircle is a = πd²/8
• The area of shaded region can be find as follow:

Area of shaded region = Area of rectangle - Area of semicircle

Area of shaded region = A - a

Area of shaded region = L² - πd²/8

Area of shaded region = 5² - (3.14×5²)/8

Area of shaded region = 25 - 9.812

Area of shaded region = 15.188 sq. yd

So the Area of shaded region will be 15.188 sq. yd

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