Intermediate Mathematics

Area of Circles

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Area of Circles

By cutting a circle into sectors and rearranging them, you can see that the area of a circle resembles the area of a parallelogram. The base of the parallelogram is same as one-half the circumference of the circle, and the height of the parallelogram is the same as the radius the circle.

Area of Circles

To find the area of any circle, multiply the length of the radius times itself times π . Use 3.14 for π .

Calculate the area of a circle with a 5 cm radius.

A = π · r²
A = 3.14 x 5 x 5
A = 78.5 cm²

The area of a circle with a 5 cm radius is 78.5 cm² or 78.5 square centimeters.

Area of Circles

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Question 1 of 10

Multiply π times the square of the radius. (A = 3.14 · r · r). Try again.

You may have forgotten to square the radius. (A = 3.14 · r · r). Try again.

3.14 × 10 × 10 = 314
The area of the circle is 314 sq. in.

You may have doubled the radius instead of squaring it.(A = 3.14 · r · r). Try again.

One of these is the result of multiplying π times the square of the radius. Try again.

This is correct formula:
A = π · r²

Area of Circles

Click on the area.

A circular rug has a radius of 3 meters. What is the area of this rug?

Question 2 of 10

3.14 × 3 × 3 = 28.26
The area of this rug is 28.26 square meters.

Muitliply π times the square of the radius. (A = 3.14 · r · r). Try again.

You may have doubled the radius instead of squaring it.(A = 3.14 · r · r). Try again.

You may have forgotten to square the radius. (A = 3.14 · r · r). Try again.

One of these is the result of multiplying π times the square of the radius. Try again.

This is correct formula:
A = π · r²

Area of Circles

Click on the area.

A helicopter landing pad is about to be paved. Using the diagram, calculate the area of the surface to be paved.

Question 3 of 10

You may have doubled the radius instead of squaring it.(A = 3.14 · r · r). Try again.

3.14 × 25 × 25 = 1962.25
The surface to be paved is 1,962.5 sq. ft.

You may have forgotten to multiply the squared radius by π. (A = 3.14 · r · r). Try again.

You may have forgotten to square the radius. (A = 3.14 · r · r). Try again.

One of these is the result of multiplying π times the square of the radius. Try again.

This is correct formula:
A = π · r²

Area of Circles

Sometimes the information given about a circle includes the length of its diameter, but not its radius. Remember that the radius is equal to one-half the length of the diameter.

A = π · r²
A = π · r · r
A = π · \(\frac{1}{2}\)d · \(\frac{1}{2}\)d

Area of Circles

To find the area of a circle when the diameter is given, follow these two steps:

1. Find the radius \(\frac{1}{2}\)·d.
2. Use the standard formula A = π · r².

The geometry teacher wishes to build a circular patio in her backyard. If the lawn that she wishes to cover is 7 meters in diameter, what will be the area of her patio?

diameter = 7 meters
radius = \(\frac{1}{2}\) × diameter = 3.5 meters

A = π · r²
A = 3.14 × 3.5 × 3.5
A = 38.465 sq. m(Rounds to 38.47)

The area of her patio will be 38.47 square meters.

Area of Circles

Click on the area.

Question 4 of 10

3.14 × 12 × 12 = 452.16
The area of this circle is 452.16 cm².

You may have used the diameter instead of squaring the radius. (A = 3.14 · r · r). Try again.

You may have doubled the diameter. You need to square the radius. (A = 3.14 · r · r). Try again.

You may have squared the diameter instead of the radius.(A = 3.14 · r · r). Try again.

One of these is the result of multiplying π times the square of the radius. Try again.

Use the radius to find the area of a circle: A = π · r²

Area of Circles

Click on the area.

A circular wading pool has a diameter of 5 feet. If the owner of the pool wish to buy a cover for it, what should the area of this cover be?

Question 5 of 10

Muitliply π times the square of the radius.
(A = 3.14 · r · r). Try again.

You may have used the diameter instead of squaring the radius. (A = 3.14 · r · r). Try again.

You may have doubled the diameter. You need to square the radius.(A = 3.14 · r · r). Try again.

You may have squared the diameter instead of the radius. (A = 3.14 · r · r). Try again.

3.14 × 2.5 × 2.5 = 19.625 (Rounds to 19.63) The area of the pool cover must be 19.63 square feet.

Use the radius to find the area of circle: A = π · r²

Area of Circles

Click on the area.

This circular flower bed needs mulching. Find the area that the gardener must cover with mulch.

Question 6 of 10

You may have used the diameter instead of squaring the radius. (A = 3.14 · r · r). Try again.

You may have squared the diameter instead of the radius.(A = 3.14 · r · r). Try again.

You may have doubled the diameter. You need to square the radius. (A = 3.14 · r · r). Try again.

3.14 × 4.5 × 4.5 = 63.585 (Rounds to 63.59) The gardener must cover 63.59 m² with mulch.

One of these is the result of multiplying π times the square of the radius. Try again.

Use the radius to find the area of circle:
A = π · r²

Area of Circles

Often it is necessary to find the area of an irregularly shaped figure.

To find the area of an irregular figure, follow these three steps:

1. Decide what simpler shapes make up the figure.
2. Find the area of the simpler shapes.
3. Subtract or add the areas to produce the irregular figure.

Area of Circles

Find the area of the irregularly shaped figure below.

Decide what simpler shapes make up the figure.

This figure is made up of a rectangle and a circle.

Area of Circles

Find the areas of the simpler shapes.


Area of the rectangle A = l · w A = 6 × 4 A = 24 sq. cm	Area of the circle A = π · r² A = 3.14 × 2 × 2 A = 12.56 sq. cm

Area of Circles

Subtract or add the areas to produce the irregular figure.

Since you are trying to find the area of the entire figure, add the areas of the rectangle and the circle.

A = area of rectangle + area of circle
A = 24 + 12.56
A = 36.56 sq. cm

The area of this irregular figure is 36.56 sq. cm.

Area of Circles

Subtract the areas of the simpler shapes when you are trying to find the area between these shapes.

Add the areas of the simpler shapes when you are trying to find the total area.

Area of Circles

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A circular fountain was placed in a park. What is the area of the remaining grass that the gardener must mow?

Question 7 of 10

You may have forgotten to subtract the area of the park covered by the fountain. No grass will remain under the fountain. Try again.

You may have added the areas. You are looking for the area between the circle and the square, so you must subtract. Try again.

Square: 50 × 50 = 2500 sq. ft.
Circle: 3.14 × 5 × 5 = 78.5 sq. ft.
2500 − 78.5 = 2421.5 sq.ft.
The gardener must mow 2,421.5 sq. ft.

You may have used the diameter of the fountain instead of its radius. Try again.

One of these is the result of subtracting the area of the fountain from the area of the park. Try again.

Subtract the area of the circle (fountain) from the area of the square (park) to find the area between these two shapes.

Area of Circles

Click on the area.

A circle with a 2 cm diameter is drawn inside a circle with a 6 cm radius. What is the area between the circles?

Question 8 of 10

You may have used the diameter when calculating the area of the inside circle.(A = 3.14 · r · r). Try again.

You may have forgotten to subtract the area of the inside circle. Try again.

Large circle: 3.14 × 6 × 6 = 113.04 cm²
Small circle: 3.14 × 1 × 1 = 3.14 cm²
113.04 − 3.14 = 109.9 cm²
The area between the circles is 109.9 cm².

You may have added the areas. You must subtract to find the area between the circles. Try again.

One of these is the result of subtracting the area of the fountain from the area of the park. Try again.

Find the area of each circle. Then subtract to find the area between the circles.

Area of Circles

Click on the area.

Calculate the amount of construction paper needed by each child to make an ice cream cone for the bulletin board.

Question 9 of 10

You may have subtracted the areas when you should have added. Try again.

You may have doubled the radius of the circle instead of squaring it. (A = 3.14 · r · r). Try again.

Circle: 3.14 × 4 × 4 = 50.24 sq. in.
Triangle: \(\color{#0a7d0a}{\frac{1}{2}}\) × 7 × 12 = 42 sq. in.
50.24 + 42 = 92.42 sq. in.
Each child needs 92.24 sq. in. of paper.

This is the area of the circle. The ice cream cone is made up of a circle and a triangle. Try again.

One of these is the result of subtracting the area of the fountain from the area of the park. Try again.

Find the area of the circle and the area of the triangle. Add the areas to find the total area.

Area of Circles

Click on the area.

Question 10 of 10

You may have used the diameter instead of the radius. (A = 3.14 · r · r). Try again.

Circle: 3.14 × 5 × 5 = 78.5 sq. cm.
Semicircle: \(\color{#0a7d0a}{\frac{1}{2}}\) × 78.5 = 39.25 sq. cm.
3 × 39.25 = 117.75 sq. in.
The area of the 3 semicircles is 117.75 sq. cm.

You may have found the area of three circles instead of three semicircles. Try again.

You may have found the area of two whole circles. Three equal semicircles only make \(\color{#be0a0a}{1\frac{1}{2}}\) circles. Try again.

One of these is the result of adding the areas of the three semicircles. Try again.

Since all of the semicircles have the same diameter,find the area of one of them and multiply by three.

Area of Circles