Area of Circles

Question 1 of 9

Find the area of the circle

Round your answer to

1

$1$ decimal place

Use

π = 3.14

$pi=3.14$

$Area =$ $\text(Area )=$ (78.5, 78.6) $c m^{2}$ $cm^2$

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Area of a Circle Formula

Area = π \times

$\text(Area)=pi times$ ${radius}^{2}$ $\text(radius)^2$

Given Lengths

radius = 5

$\text(radius)=5$

Solve for the area using the formula:

A = π

$A=pi$ $r^{2}$ $r^2$

Use

π = 3.14

$pi=3.14$ See

π

$pi$ explained

$Area$ $\text(Area)$	$=$ $=$	$π \times$ $pi times$ ${radius}^{2}$ $\text(radius)^2$	Area of a Circle Formula
	$=$ $=$	$3.14 \times$ $3.14 times$ $5^{2}$ $5^2$	Plug in the known values
	$=$ $=$	$3.14 \times 25$ $3.14 times 25$	Evaluate
	$=$ $=$	$78.5 c m^{2}$ $78.5 cm^2$

The given measurements are in centimetres, so the area is measured as square centimetres

Area = 78.5 c m^{2}

$\text(Area)=78.5 cm^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.14

$pi=3.14$ .

Using	Answer
$π = 3.14$ $pi=3.14$	$78.5 c m^{2}$ $78.5 cm^2$
$π = 3.141592654$ $pi=3.141592654$	$78.5 c m^{2}$ $78.5 cm^2$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$78.6 c m^{2}$ $78.6 cm^2$

Question 2 of 9

Find the area of the Circle

Round your answer to

1

$1$ decimal place

Use

π = 3.141592654

$pi=3.141592654$

$Area =$ $\text(Area )=$ (254.5, 254.3, 254.6) $m m^{2}$ $mm^2$

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Area of a Circle Formula

Area = π \times

$\text(Area)=pi times$ ${radius}^{2}$ $\text(radius)^2$

Given Lengths

diameter = 18

$\text(diameter)=18$

First, find the radius of the circle. Note that the radius is half of the diameter.

$radius$ $\text(radius)$	$=$ $=$	$\frac{\color{#00880a}{\text{diameter}}}{2}$

	$=$ $=$	$\frac{\color{#00880a}{\text{18}}}{2}$

$radius$ $\text(radius)$	$=$ $=$	$9$ $9$

Finally, solve for the area using the formula:

A = π

$A=pi$ $r^{2}$ $r^2$

Use

π = 3.141592654

$pi=3.141592654$ See

π

$pi$ explained

$Area$ $\text(Area)$	$=$ $=$	$π \times$ $pi times$ ${radius}^{2}$ $\text(radius)^2$	Area of a Circle Formula
	$=$ $=$	$3.141592654 \times$ $3.141592654 times$ $9^{2}$ $9^2$	Plug in the known values
	$=$ $=$	$3.141592654 \times 81$ $3.141592654 times 81$	Evaluate
	$=$ $=$	$254.46900$ $254.46900$
	$=$ $=$	$254.5 m m^{2}$ $254.5 mm^2$	Rounded to $1$ $1$ decimal place

The given measurements are in millimetres, so the area is measured as square millimetres

Area = 254.5 m m^{2}

$\text(Area)=254.5 mm^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.141592654

$pi=3.141592654$ .

Using	Answer
$π = 3.141592654$ $pi=3.141592654$	$254.5 m m^{2}$ $254.5 mm^2$
$π = 3.14$ $pi=3.14$	$254.3 m m^{2}$ $254.3 mm^2$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$254.6 m m^{2}$ $254.6 mm^2$

Question 3 of 9

Find the area of the circle

Round your answer to

1

$1$ decimal place

Use

π = 3.14

$pi=3.14$

$Area =$ $\text(Area )=$ (346.2, 346.4, 346.5) $m^{2}$ $m^2$

Incorrect

Area of a Circle Formula

Area = π \times

$\text(Area)=pi times$ ${radius}^{2}$ $\text(radius)^2$

Given Lengths

diameter = 21

$\text(diameter)=21$

First, find the radius of the circle. Note that the radius is half of the diameter

$radius$ $\text(radius)$	$=$ $=$	$\frac{\color{#00880a}{\text{diameter}}}{2}$

	$=$ $=$	$\frac{\color{#00880a}{\text{21}}}{2}$

$radius$ $\text(radius)$	$=$ $=$	$10.5$ $10.5$

Finally, solve for the area using the formula:

A = π

$A=pi$ $r^{2}$ $r^2$

Use

π = 3.14

$pi=3.14$ See

π

$pi$ explained

$Area$ $\text(Area)$	$=$ $=$	$π \times$ $pi times$ ${radius}^{2}$ $\text(radius)^2$	Area of a Circle Formula
	$=$ $=$	$3.14 \times$ $3.14 times$ ${10.5}^{2}$ $10.5^2$	Plug in the known values
	$=$ $=$	$3.14 \times 110.25$ $3.14 times 110.25$	Evaluate
	$=$ $=$	$346.185$ $346.185$
	$=$ $=$	$346.2 m^{2}$ $346.2 m^2$	Rounded to $1$ $1$ decimal place

The given measurements are in metres, so the area is measured as square metres

Area = 346.2 m^{2}

$\text(Area)=346.2 m^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.14

$pi=3.14$ .

Using	Answer
$π = 3.14$ $pi=3.14$	$346.2 m^{2}$ $346.2 m^2$
$π = 3.141592654$ $pi=3.141592654$	$346.4 m^{2}$ $346.4 m^2$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$346.5 m^{2}$ $346.5 m^2$

Question 4 of 9

Find the area of the Circle

Round your answer to

1

$1$ decimal place

Use

π = 3.14

$pi=3.14$

$Area =$ $\text(Area )=$ (452.2, 452.4, 452.6) $m^{2}$ $m^2$

Incorrect

Area of a Circle Formula

Area = π \times

$\text(Area)=pi times$ ${radius}^{2}$ $\text(radius)^2$

Given Lengths

diameter = 24

$\text(diameter)=24$

First, find the radius of the circle. Note that the radius is half of the diameter

$radius$ $\text(radius)$	$=$ $=$	$\frac{\color{#00880a}{\text{diameter}}}{2}$

	$=$ $=$	$\frac{\color{#00880a}{\text{24}}}{2}$

$radius$ $\text(radius)$	$=$ $=$	$12$ $12$

Finally, solve for the area using the formula:

A = π

$A=pi$ $r^{2}$ $r^2$

Use

π = 3.14

$pi=3.14$ See

π

$pi$ explained

$Area$ $\text(Area)$	$=$ $=$	$π \times$ $pi times$ ${radius}^{2}$ $\text(radius)^2$	Area of a Circle Formula
	$=$ $=$	$3.14 \times$ $3.14 times$ $12^{2}$ $12^2$	Plug in the known values
	$=$ $=$	$3.14 \times 144$ $3.14 times 144$	Evaluate
	$=$ $=$	$452.16$ $452.16$
	$=$ $=$	$452.2 m^{2}$ $452.2 m^2$	Rounded to $1$ $1$ decimal place

The given measurements are in metres, so the area is measured as square metres

Area = 452.2 m^{2}

$\text(Area)=452.2 m^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.14

$pi=3.14$ .

Using	Answer
$π = 3.14$ $pi=3.14$	$452.2 m^{2}$ $452.2 m^2$
$π = 3.141592654$ $pi=3.141592654$	$452.4 m^{2}$ $452.4 m^2$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$452.6 m^{2}$ $452.6 m^2$

Question 5 of 9

Find the area of the Circle

Round your answer to

1

$1$ decimal place

Use

π = 3.14

$pi=3.14$

$Area =$ $\text(Area )=$ (149.5, 149.6) $k m^{2}$ $km^2$

Incorrect

Area of a Circle Formula

Area = π \times

$\text(Area)=pi times$ ${radius}^{2}$ $\text(radius)^2$

Given Lengths

diameter = 13.8

$\text(diameter)=13.8$

First, find the radius of the circle
Note that the radius is half of the diameter

$radius$ $\text(radius)$	$=$ $=$	$\frac{\color{#00880a}{\text{diameter}}}{2}$

	$=$ $=$	$\frac{\color{#00880a}{\text{13.8}}}{2}$

$radius$ $\text(radius)$	$=$ $=$	$6.9$ $6.9$

Finally, solve for the area using the formula:

A = π

$A=pi$ $r^{2}$ $r^2$

Use

π = 3.14

$pi=3.14$ See

π

$pi$ explained

$Area$ $\text(Area)$	$=$ $=$	$π \times$ $pi times$ ${radius}^{2}$ $\text(radius)^2$	Area of a Circle Formula
	$=$ $=$	$3.14 \times$ $3.14 times$ ${6.9}^{2}$ $6.9^2$	Plug in the known values
	$=$ $=$	$3.14 \times 47.61$ $3.14 times 47.61$	Evaluate
	$=$ $=$	$149.4954$ $149.4954$
	$=$ $=$	$149.5 k m^{2}$ $149.5 km^2$	Rounded to $1$ $1$ decimal place

The given measurements are in kilometres, so the area is measured as square kilometres

Area = 149.5 k m^{2}

$\text(Area)=149.5 km^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.14

$pi=3.14$ .

Using	Answer
$π = 3.14$ $pi=3.14$	$149.5 k m^{2}$ $149.5 km^2$
$π = 3.141592654$ $pi=3.141592654$	$149.6 k m^{2}$ $149.6 km^2$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$149.6 k m^{2}$ $149.6 km^2$

Question 6 of 9

Find the area of the Circle

Round your answer to

1

$1$ decimal place

Use

π = 3.14

$pi=3.14$

$Area =$ $\text(Area )=$ (12.6) $c m^{2}$ $cm^2$

Incorrect

Area of a Circle Formula

Area = π \times

$\text(Area)=pi times$ ${radius}^{2}$ $\text(radius)^2$

Given Lengths

diameter = 4

$\text(diameter)=4$

First, find the radius of the circle
Note that the radius is half of the diameter

$radius$ $\text(radius)$	$=$ $=$	$\frac{\color{#00880a}{\text{diameter}}}{2}$

	$=$ $=$	$\frac{\color{#00880a}{\text{4}}}{2}$

$radius$ $\text(radius)$	$=$ $=$	$2$ $2$

Finally, solve for the area using the formula:

A = π

$A=pi$ $r^{2}$ $r^2$

Use

π = 3.14

$pi=3.14$ See

π

$pi$ explained

$Area$ $\text(Area)$	$=$ $=$	$π \times$ $pi times$ ${radius}^{2}$ $\text(radius)^2$	Area of a Circle Formula
	$=$ $=$	$3.14 \times$ $3.14 times$ $2^{2}$ $2^2$	Plug in the known values
	$=$ $=$	$3.14 \times 4$ $3.14 times 4$	Evaluate
	$=$ $=$	$12.56$ $12.56$
	$=$ $=$	$12.6 c m^{2}$ $12.6 cm^2$	Rounded to $1$ $1$ decimal place

The given measurements are in centimetres, so the area is measured as square centimetres

Area = 12.6 c m^{2}

$\text(Area)=12.6 cm^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.14

$pi=3.14$ .

Using	Answer
$π = 3.14$ $pi=3.14$	$12.6 c m^{2}$ $12.6 cm^2$
$π = 3.141592654$ $pi=3.141592654$	$12.6 c m^{2}$ $12.6 cm^2$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$12.6 c m^{2}$ $12.6 cm^2$

Question 7 of 9

Find the area of the orange-shaded region.

The given measurements are in centimetres.

Round your answer to

1

$1$ decimal place.

π = 3.14

$pi=3.14$

$Area =$ $\text(Area )=$ (103.7, 103.6) $c m^{2}$ $cm^2$

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Area of a Circle Formula

Area = π \times

$\text(Area)=pi xx$ ${radius}^{2}$ $\text(radius)^2$

Given Lengths

radius

$\text(radius)$ (Whole Circle)

= 7

$=7$

thickness

$\text(thickness)$ (Shaded Region)

= 3

$=3$

First, solve for the area of the Whole Circle

Use

π = 3.14

$pi=3.14$ See

π

$pi$ explained

$Area$ $\text(Area)$ _{$Whole Circle$ $\text(Whole Circle)$}	$=$ $=$	$π \times$ $pi xx$ ${radius}^{2}$ $\text(radius)^2$
	$=$ $=$	$3.14 \times$ $3.14 xx$ $7^{2}$ $7^2$
$Area$ $\text(Area)$	$=$ $=$	$153.86 c m^{2}$ $153.86 cm^2$

Find the radius of the Inner Circle by subtracting the thickness of the shaded region from the radius of the Whole Circle.

$radius$ $\text(radius)$ _{$Inner Circle$ $\text(Inner Circle)$}	$=$ $=$	$radius$ $\text(radius)$ $-$ $-$ $thickness$ $\text(thickness)$
	$=$ $=$	$7$ $7$ $-$ $-$ $3$ $3$
	$=$ $=$	$4 c m$ $4 cm$

Next, find the area of the Inner Circle

$Area$ $\text(Area)$ _{$Inner Circle$ $\text(Inner Circle)$}	$=$ $=$	$π \times$ $pi xx$ ${radius}^{2}$ $\text(radius)^2$
	$=$ $=$	$3.14 \times$ $3.14 times$ $4^{2}$ $4^2$
$Area$ $\text(Area)$	$=$ $=$	$50.24 c m^{2}$ $50.24 cm^2$

Finally, subtract the area of the Inner Circle from the area of the Whole Circle

$Final Area$ $\text(Final Area)$	$=$ $=$	$153.86$ $153.86$ $-$ $-$ $50.24$ $50.24$
	$=$ $=$	$103.62$ $103.62$
	$=$ $=$	$103.6 c m^{2}$ $103.6 cm^2$	Rounded to $1$ $1$ decimal place

The given measurements are in centimetres, so the area is measured as square centimetres

Area = 103.6 c m^{2}

$\text(Area)=103.6 cm^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.14

$pi=3.14$ .

Using	Answer
$π = 3.14$ $pi=3.14$	$103.6 c m^{2}$ $103.6 cm^2$
$π = 3.141592654$ $pi=3.141592654$	$103.7 c m^{2}$ $103.7 cm^2$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$103.7 c m^{2}$ $103.7 cm^2$

Question 8 of 9

Find the area of the yellow-shaded region.

Round your answer to

1

$1$ decimal place

Use

π = 3.14

$pi=3.14$

$Area =$ $\text(Area )=$ (50.2, 50.3) $c m^{2}$ $cm^2$

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Area of a Semicircle Formula

Area = \frac{1}{2} \times π \times

$\text(Area)=1/2 xx pi xx$ ${radius}^{2}$ $\text(radius)^2$

Given Lengths

radius

$\text(radius)$ (Whole Semicircle)

= 9

$=9$

thickness

$\text(thickness)$ (Shaded Region)

= 2

$=2$

First, solve for the area of the Whole Semicircle

Use

π = 3.14

$pi=3.14$ See

π

$pi$ explained

$Area$ $\text(Area)$ _{$Whole Semicircle$ $\text(Whole Semicircle)$}	$=$ $=$	$\frac{1}{2} \times π \times$ $1/2 xx pi xx$ ${radius}^{2}$ $\text(radius)^2$
	$=$ $=$	$\frac{1}{2} \times 3.14 \times$ $1/2 xx 3.14 xx$ $9^{2}$ $9^2$
$Area$ $\text(Area)$	$=$ $=$	$127.17 c m^{2}$ $127.17 cm^2$

Find the radius of the Inner Semicircle by subtracting the thickness of the shaded region from the radius of the Whole Semicircle.

$radius$ $\text(radius)$ _{$Inner Semicircle$ $\text(Inner Semicircle)$}	$=$ $=$	$radius$ $\text(radius)$ $-$ $-$ $thickness$ $\text(thickness)$
	$=$ $=$	$9$ $9$ $-$ $-$ $2$ $2$
	$=$ $=$	$7 c m$ $7 cm$

Next, find the area of the Inner Semicircle

$Area$ $\text(Area)$ _{$Inner Semicircle$ $\text(Inner Semicircle)$}	$=$ $=$	$\frac{1}{2} \times π \times$ $1/2 xx pi xx$ ${radius}^{2}$ $\text(radius)^2$
	$=$ $=$	$\frac{1}{2} \times 3.14 \times$ $1/2 xx 3.14 times$ $7^{2}$ $7^2$
$Area$ $\text(Area)$	$=$ $=$	$76.93 c m^{2}$ $76.93 cm^2$

Finally, subtract the area of the Inner Semicircle from the area of the Whole Semicircle

$Final Area$ $\text(Final Area)$	$=$ $=$	$127.17$ $127.17$ $-$ $-$ $76.93$ $76.93$
	$=$ $=$	$50.24$ $50.24$
	$=$ $=$	$50.2 c m^{2}$ $50.2 cm^2$	Rounded to $1$ $1$ decimal place

The given measurements are in centimetres, so the area is measured as square centimetres

Area = 50.2 c m^{2}

$\text(Area)=50.2 cm^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.14

$pi=3.14$ .

Using	Answer
$π = 3.14$ $pi=3.14$	$50.2 c m^{2}$ $50.2 cm^2$
$π = 3.141592654$ $pi=3.141592654$	$50.3 c m^{2}$ $50.3 cm^2$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$50.3 c m^{2}$ $50.3 cm^2$

Question 9 of 9

Find the area of the yellow-shaded region.

Round your answer to

2

$2$ decimal places

Use

π = 3.141592654

$pi=3.141592654$

$Area =$ $\text(Area )=$ (96.21, 96.16, 96.25) $m^{2}$ $m^2$

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Area of a Semicircle Formula

Area = \frac{1}{2} \times π \times

$\text(Area)=1/2 xx pi xx$ ${radius}^{2}$ $\text(radius)^2$

Given Lengths

radius

$\text(radius)$ (Larger Semicircle)

= 7

$=7$

diameter

$\text(diameter)$ (Smaller Semicircle)

= 7

$=7$

First, solve for the area of the Larger Semicircle

Use

π = 3.141592654

$pi=3.141592654$ See

π

$pi$ explained

$Area$ $\text(Area)$ _{$Larger Semicircle$ $\text(Larger Semicircle)$}	$=$ $=$	$\frac{1}{2} \times π \times$ $1/2 xx pi xx$ ${radius}^{2}$ $\text(radius)^2$
	$=$ $=$	$\frac{1}{2} \times 3.141592654 \times$ $1/2 xx 3.141592654 xx$ $7^{2}$ $7^2$
$Area$ $\text(Area)$	$=$ $=$	$76.96902 m^{2}$ $76.96902 m^2$

We can see on the image that the diameter of the Smaller Semicircle is

7

$7$

We will use that to solve for the radius of the Smaller Semicircle, which is half of its diameter

$radius$ $\text(radius)$ _{$Smaller Semicircle$ $\text(Smaller Semicircle)$}	$=$ $=$	$\frac{\color{#00880a}{\text{diameter}}}{2}$
	$=$ $=$	$\frac{\color{#00880a}{\text{7}}}{2}$
	$=$ $=$	$3.5 m$ $3.5 m$

Next, find the area of the Smaller Semicircle

$Area$ $\text(Area)$ _{$Smaller Semicircle$ $\text(Smaller Semicircle)$}	$=$ $=$	$\frac{1}{2} \times π \times$ $1/2 xx pi xx$ ${radius}^{2}$ $\text(radius)^2$
	$=$ $=$	$\frac{1}{2} \times 3.141592654 \times$ $1/2 xx 3.141592654 times$ ${3.5}^{2}$ $3.5^2$
$Area$ $\text(Area)$	$=$ $=$	$19.24225 m^{2}$ $19.24225 m^2$

Finally, add the area of the Larger Semicircle and the area of the Smaller Semicircle

$Final Area$ $\text(Final Area)$	$=$ $=$	$76.96902$ $76.96902$ $+$ $+$ $19.24225$ $19.24225$
	$=$ $=$	$96.21127$ $96.21127$
	$=$ $=$	$96.21 m^{2}$ $96.21 m^2$	Rounded to $2$ $2$ decimal places

The given measurements are in metres, so the area is measured as square metres

Area = 96.21 m^{2}

$\text(Area)=96.21 m^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.141592654

$pi=3.141592654$ .

Using	Answer
$π = 3.141592654$ $pi=3.141592654$	$96.21 m^{2}$ $96.21 m^2$
$π = 3.14$ $pi=3.14$	$96.16 m^{2}$ $96.16 m^2$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$96.25 m^{2}$ $96.25 m^2$

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Quiz summary

Information

1. Question

Hint

Well Done!

Area of a Circle Formula

Given Lengths

2. Question

Hint

Nice Job!

Area of a Circle Formula

Given Lengths

3. Question

Great Work!

Area of a Circle Formula

Given Lengths

4. Question

Correct!

Area of a Circle Formula

Given Lengths

5. Question

Keep Going!

Area of a Circle Formula

Given Lengths

6. Question

Fantastic!

Area of a Circle Formula

Given Lengths

7. Question

Hint

Correct!

Area of a Circle Formula

Given Lengths

8. Question

Hint

Fantastic!

Area of a Semicircle Formula

Given Lengths

9. Question

Hint

Area of a Semicircle Formula

Given Lengths

Quizzes