Circles Problem Solving

This figure shows two semicircles connected perfectly to a rectangle along their diameters.

What is the approximate area of the figure? Use 3.14 for pi.

• 117.2 ft²

• 136.5 ft²

• 142.0 ft²

• 251.9 ft²

Answer explanation

If the diameter of the semicircles is 7 ft, then the radius is 3.5 ft.

Since there are two semicircles, you can put them together and find the area of a single circle with a radius of 3.5 ft. Use the formula A = π r².

Add the circle area to the rectangle area for the final answer.

A circular flower garden has a diameter of 16 ft. A square pond is placed in the center that measures 5 feet on each side. About how much of the garden remains for planting flowers? Use 3.14 for pi.

• 75 ft²

• 176 ft²

• 226 ft²

• 779 ft²

Answer explanation

You essentially need to find two areas and subtract them to solve this problem.

Circle area - square area = answer

Be careful while calculating the circle area, as the formula is A = π r², and they gave you the diameter of 16 ft.

The square has sides of 5 ft, so use those to find the square area.

The diagram below shows the remodeling of Sam's backyard patio. He has removed two congruent semicircle sections for flower gardens. The diameter of each of the semicircle sections is 2 meters. What is the approximate area of the patio now? Use 3.14 for pi.

• 50 m²

• 54 m²

• 57 m²

• 60 m²

Answer explanation

This problem is essentially a subtraction problem. If you combine the two semi-circles, you can find their area as just one circle with A = π r². Be careful, as you need to use the radius of the circle, not the given diameter of 2 m.

Rectangle area - circle area = answer

The diagram shows a section of the playground that has been marked off in a triangle as a dance area for the school carnival. The center circle will be a special spotlight area with a diameter of 8 feet. What is the approximate area of the shaded portion? Use 3.14 for pi.

• 27 square feet

• 178 square feet

• 228 square feet

• 405 square feet

Answer explanation

This is essentially a subtraction problem. Take the triangle area and subtract the circle area.

Be careful to remember that triangle area is $A\ =\ \frac{1}{2}bh$ and to remember to use the radius of the circle when calculating the circle area with A = π r².

The given diameter is 8 feet.

This is a drawing of Lane's swimming pool. The pool is rectangular with a semi-circular end.
What is the approximate area of Lane's pool? Use 3.14 for pi.

• 1,000 m²

• 1,628 m²

• 2,256 m²

• 3,512 m²

Answer explanation

First of all, you can split the image into the rectangle and semicircle. That should show you that the 25 m is only the rectangle length, not a part of the semicircle. If the diameter of the semicircle is 40 m, the radius is 20 m.

The formula for the area off a semicircle is $A\ =\ \frac{1}{2}\pi\ r^2$ . Find the area of the semicircle.

Now, add to that area the area of the rectangle.

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