Area of Composite Shapes

Question 1 of 5

Find the area of the shape.

The given measurements are in centimetres

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

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Area of a Rectangle Formula

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

Identify the known lengths

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

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

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

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

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

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

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

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

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

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

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

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

Question 2 of 5

Find the area of the shape.

The given measurements are in metres

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

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Area of a Rectangle Formula

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

Identify the known lengths

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

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

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

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

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

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

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

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

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

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

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

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

Question 3 of 5

Find the area of the shape.

The given measurements are in centimetres

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

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Area of a Rectangle Formula

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

Identify the known lengths

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

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

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

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

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

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

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

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

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

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

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

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

Question 4 of 5

Find the area of the shape.

The given measurements are in centimetres

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

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Area of a Rectangle Formula

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

$times$ $\text(width)$

Area of a Triangle Formula

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

$times$ $\text(height)$

Identify the known lengths

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

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

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

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

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

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

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

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

	$=$	$1/2$ $20$ $times$ $10$	Plug in the known values

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

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

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

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

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

Question 5 of 5

Find the area of the shape.

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

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

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Area of a Rectangle Formula

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

$times$ $\text(width)$

Area of a Semicircle Formula

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

Identify the known lengths

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

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

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

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

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

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

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

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

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

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

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

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

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

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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