Area of Composite Shapes

Question 1 of 5

Find the area of the shape.

The given measurements are in centimetres

$Area =$ $\text(Area )=$ (420) ${cm}^{2}$ $\text(cm)^2$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Area of a Rectangle Formula

Area = length \times width

$\text(Area )=\text(length) times \text(width)$

Identify the known lengths

$length$ $\text(length)$ (Larger Rectangle) $= 22$ $=22$

$width$ $\text(width)$ (Larger Rectangle) $= 10$ $=10$

$length$ $\text(length)$ (Smaller Rectangle) $= 10$ $=10$

$width$ $\text(width)$ (Smaller Rectangle) $= 30 - 10 = 20$ $=30-10=20$

First, solve for the area of the Larger Rectangle using the formula

$Area$ $\text(Area)$ _{$Larger Rectangle$ $\text(Larger Rectangle)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $width$ $\text(width)$	Area of a Rectangle Formula
	$=$ $=$	$10$ $10$ $\times$ $times$ $22$ $22$	Plug in the known values
$Area$ $\text(Area)$ _{$Larger Rectangle$ $\text(Larger Rectangle)$}	$=$ $=$	$220 {cm}^{2}$ $220 \text(cm)^2$

Next, solve for the area of the Smaller Rectangle using the formula

$Area$ $\text(Area)$ _{$Smaller Rectangle$ $\text(Smaller Rectangle)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $width$ $\text(width)$	Area of a Rectangle Formula
	$=$ $=$	$10$ $10$ $\times$ $times$ $20$ $20$	Plug in the known values
$Area$ $\text(Area)$ _{$Smaller Rectangle$ $\text(Smaller Rectangle)$}	$=$ $=$	$200 {cm}^{2}$ $200 \text(cm)^2$

Finally, get the final area by adding the area of the
Smaller Rectangle to the area of the Larger Rectangle

$\text{Total Area}$	$=$ $=$	$220$ $220$ $+$ $+$ $200$ $200$	Plug in the known values
	$=$ $=$	$420 {cm}^{2}$ $420 \text(cm)^2$

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

Area = 420 {cm}^{2}

$\text(Area)=420 \text(cm)^2$

Question 2 of 5

Find the area of the shape.

The given measurements are in metres

$Area =$ $\text(Area )=$ (156) $m^{2}$ $\text(m)^2$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Area of a Rectangle Formula

Area = length \times width

$\text(Area )=\text(length) times \text(width)$

Identify the known lengths

$length$ $\text(length)$ (Larger Rectangle) $= 20$ $=20$

$width$ $\text(width)$ (Larger Rectangle) $= 5$ $=5$

$length$ $\text(length)$ (Smaller Rectangle) $= 4$ $=4$

$width$ $\text(width)$ (Smaller Rectangle) $= 14$ $=14$

First, solve for the area of the Larger Rectangle using the formula

$Area$ $\text(Area)$ _{$Larger Rectangle$ $\text(Larger Rectangle)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $width$ $\text(width)$	Area of a Rectangle Formula
	$=$ $=$	$20$ $20$ $\times$ $times$ $5$ $5$	Plug in the known values
$Area$ $\text(Area)$ _{$Larger Rectangle$ $\text(Larger Rectangle)$}	$=$ $=$	$100 m^{2}$ $100 \text(m)^2$

Next, solve for the area of the Smaller Rectangle using the formula

$Area$ $\text(Area)$ _{$Smaller Rectangle$ $\text(Smaller Rectangle)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $width$ $\text(width)$	Area of a Rectangle Formula
	$=$ $=$	$4$ $4$ $\times$ $times$ $14$ $14$	Plug in the known values
$Area$ $\text(Area)$ _{$Smaller Rectangle$ $\text(Smaller Rectangle)$}	$=$ $=$	$56 m^{2}$ $56 \text(m)^2$

Finally, get the final area by adding the area of the
Smaller Rectangle to the area of the Larger Rectangle

$\text{Total Area}$	$=$ $=$	$100$ $100$ $+$ $+$ $56$ $56$	Plug in the known values
	$=$ $=$	$156 m^{2}$ $156 \text(m)^2$

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

Area = 156 m^{2}

$\text(Area)=156 \text(m)^2$

Question 3 of 5

Find the area of the shape.

The given measurements are in centimetres

$Area =$ $\text(Area )=$ (10000) ${cm}^{2}$ $\text(cm)^2$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Area of a Rectangle Formula

Area = length \times width

$\text(Area )=\text(length) times \text(width)$

Identify the known lengths

$length$ $\text(length)$ (Larger Rectangles) $= 100$ $=100$

$width$ $\text(width)$ (Larger Rectangles) $= 40$ $=40$

$length$ $\text(length)$ (Smaller Rectangle) $= 100 - 2 (30) = 40$ $=100-2(30)=40$

$width$ $\text(width)$ (Smaller Rectangle) $= 50$ $=50$

First, solve for the area of the two Larger Rectangles using the formula

$Area$ $\text(Area)$ _{$Larger Rectangles$ $\text(Larger Rectangles)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $width$ $\text(width)$	Area of a Rectangle Formula
	$=$ $=$	$100$ $100$ $\times$ $times$ $40$ $40$	Plug in the known values
$Area$ $\text(Area)$ _{$Larger Rectangles$ $\text(Larger Rectangles)$}	$=$ $=$	$4000 {cm}^{2}$ $4000 \text(cm)^2$

Next, solve for the area of the Smaller Rectangle using the formula

$Area$ $\text(Area)$ _{$Smaller Rectangle$ $\text(Smaller Rectangle)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $width$ $\text(width)$	Area of a Rectangle Formula
	$=$ $=$	$40$ $40$ $\times$ $times$ $50$ $50$	Plug in the known values
$Area$ $\text(Area)$ _{$Smaller Rectangle$ $\text(Smaller Rectangle)$}	$=$ $=$	$2000 {cm}^{2}$ $2000 \text(cm)^2$

Finally, get the final area by adding the area of the
Smaller Rectangle to the area of the two Larger Rectangles

$\text{Total Area}$	$=$ $=$	$2 ($ $2($ $4000$ $4000$ $) +$ $)+$ $2000$ $2000$	Plug in the known values
	$=$ $=$	$10000 {cm}^{2}$ $10 000 \text(cm)^2$

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

Area = 10000 {cm}^{2}

$\text(Area)=10 000 \text(cm)^2$

Question 4 of 5

Find the area of the shape.

The given measurements are in centimetres

$Area =$ $\text(Area )=$ (800) ${cm}^{2}$ $\text(cm)^2$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Area of a Rectangle Formula

Area =

$\text(Area )=$ $length$ $\text(length)$

\times

$times$ $width$ $\text(width)$

Area of a Triangle Formula

Area = \frac{1}{2} \times

$\text(Area )=1/2times$ $base$ $\text(base)$

\times

$times$ $height$ $\text(height)$

Identify the known lengths

$length$ $\text(length)$ (Rectangle) $= 30$ $=30$

$width$ $\text(width)$ (Rectangle) $= 20$ $=20$

$base$ $\text(base)$ (Triangle) $= 20$ $=20$

$height$ $\text(height)$ (Triangle) $= 10$ $=10$

First, solve for the area of the Rectangle using the formula

$Area$ $\text(Area)$ _{$Rectangle$ $\text(Rectangle)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $width$ $\text(width)$	Area of a Rectangle Formula
	$=$ $=$	$30$ $30$ $\times$ $times$ $20$ $20$	Plug in the known values
$Area$ $\text(Area)$ _{$Rectangle$ $\text(Rectangle)$}	$=$ $=$	$600 {cm}^{2}$ $600 \text(cm)^2$

Next, solve for the area of the Triangles using the formula

$Area$ $\text(Area)$ _{$Triangle$ $\text(Triangle)$}	$=$ $=$	$\frac{1}{2}$ $1/2$ $base$ $\text(base)$ $\times$ $times$ $height$ $\text(height)$	Area of a Rectangle Formula

	$=$ $=$	$\frac{1}{2}$ $1/2$ $20$ $20$ $\times$ $times$ $10$ $10$	Plug in the known values

$Area$ $\text(Area)$ _{$Triangle$ $\text(Triangle)$}	$=$ $=$	$100 {cm}^{2}$ $100 \text(cm)^2$

Finally, get the final area by adding the area of the
two Triangles to the area of the Rectangle

$\text{Total Area}$	$=$ $=$	$600$ $600$ $+ 2 ($ $+2($ $100$ $100$ $)$ $)$	Plug in the known values
	$=$ $=$	$800 {cm}^{2}$ $800 \text(cm)^2$

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

Area = 800 {cm}^{2}

$\text(Area)=800 \text(cm)^2$

Question 5 of 5

Find the area of the shape.

The given measurements are in metres
Round your answer to two decimal paces

$Area =$ $\text(Area )=$ (199.23) $m^{2}$ $\text(m)^2$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Area of a Rectangle Formula

Area =

$\text(Area )=$ $length$ $\text(length)$

\times

$times$ $width$ $\text(width)$

Area of a Semicircle Formula

Area = \frac{1}{2} \times π \times

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

Identify the known lengths

$length$ $\text(length)$ (Rectangle) $= 18$ $=18$

$width$ $\text(width)$ (Rectangle) $= 4$ $=4$

$radius$ $\text(radius)$ (Triangle) $= 18 \div 2 = 9$ $=18divide2=9$

First, solve for the area of the Rectangle using the formula

$Area$ $\text(Area)$ _{$Rectangle$ $\text(Rectangle)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $width$ $\text(width)$	Area of a Rectangle Formula
	$=$ $=$	$18$ $18$ $\times$ $times$ $4$ $4$	Plug in the known values
$Area$ $\text(Area)$ _{$Rectangle$ $\text(Rectangle)$}	$=$ $=$	$72 m^{2}$ $72 \text(m)^2$

Next, solve for the area of the Semicircle using the formula

$Area$ $\text(Area)$ _{$Semicircle$ $\text(Semicircle)$}	$=$ $=$	$\frac{1}{2} \times π \times$ $1/2 times pi times$ ${radius}^{2}$ $\text(radius)^2$	Area of a Rectangle Formula

	$=$ $=$	$\frac{1}{2} \times π \times$ $1/2 times pi times$ $9^{2}$ $\text(9)^2$	Plug in the known values

$Area$ $\text(Area)$ _{$Triangle$ $\text(Triangle)$}	$=$ $=$	$127.23 m^{2}$ $127.23 \text(m)^2$	Rounded to two decimal places

Finally, get the final area by adding the area of the
Semicircle to the area of the Rectangle

$\text{Total Area}$	$=$ $=$	$72$ $72$ $+$ $+$ $127.23$ $127.23$	Plug in the known values
	$=$ $=$	$199.23 m^{2}$ $199.23 \text(m)^2$

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

Area = 199.23 m^{2}

$\text(Area)=199.23 \text(m)^2$

Area of Composite Shapes

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Well Done!

Area of a Rectangle Formula

Identify the known lengths

2. Question

Hint

Nice Job!

Area of a Rectangle Formula

Identify the known lengths

3. Question

Hint

Excellent!

Area of a Rectangle Formula

Identify the known lengths

4. Question

Hint

Fantastic!

Area of a Rectangle Formula

Area of a Triangle Formula

Identify the known lengths

5. Question

Hint

Exceptional!

Area of a Rectangle Formula

Area of a Semicircle Formula

Identify the known lengths

Quizzes