Areas of a Shaded Region

Question 1 of 4

Find the area of the black-shaded region.

$\text(Area )=$ (120) $cm^2$

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Area of a Square Formula

$\text(Area )=\text(side) times \text(side)$

In a regular square, all sides are equal

Identify the known lengths

$\text(side)$ (Larger Square) $=13$

$\text(side)$ (Smaller Square) $=7$

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

$\text(Area)$ _{$\text(Larger Square)$}	$=$	$\text(side)$ $times$ $\text(side)$	Area of a Square Formula
	$=$	$13$ $times$ $13$	Plug in the known values
$\text(Area)$ _{$\text(Larger Square)$}	$=$	$169 cm^2$

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

$\text(Area)$ _{$\text(Smaller Square)$}	$=$	$\text(side)$ $times$ $\text(side)$	Area of a Square Formula
	$=$	$7$ $times$ $7$	Plug in the known values
$\text(Area)$ _{$\text(Smaller Square)$}	$=$	$49 cm^2$

Finally, get the final area by subtracting the area of the
Smaller Square from the area of the Larger Square

$\text{Final Area}$	$=$	$169$ $-$ $49$	Plug in the known values
	$=$	$120 cm^2$

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

$\text(Area)=120 cm^2$

Question 2 of 4

Find the area of the pink-shaded region.

The given measurements are in metres

$\text(Area )=$ (154) $m^2$

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Area of a Rectangle Formula

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

Identify the known lengths

$\text(length)$ (Larger Rectangle) $=17$

$\text(width)$ (Larger Rectangle) $=12$

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

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

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
	$=$	$17$ $times$ $12$	Plug in the known values
$\text(Area)$ _{$\text(Larger Rectangle)$}	$=$	$204 m^2$

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
	$=$	$10$ $times$ $5$	Plug in the known values
$\text(Area)$ _{$\text(Smaller Rectangle)$}	$=$	$50 m^2$

Finally, get the final area by subtracting the area of the
Smaller Rectangle from the area of the Larger Rectangle

$\text{Total Area}$	$=$	$204$ $-$ $50$	Plug in the known values
	$=$	$154 m^2$

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

$\text(Area)=154 m^2$

Question 3 of 4

Find the area of the blue-shaded region.

$\text(Area )=$ (140) $cm^2$

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Area of a Rectangle Formula

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

$times$ $\text(width)$

Area of a Triangle Formula

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

$times$ $\text(height)$

Identify the known lengths

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

$\text(width)=\text(height)=14$

In order to find the area of the shaded region, subtract the
area of the Triangle from the area of the Rectangle.

[Rectangle – Triangle = Blue Region]

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
	$=$	$20$ $times$ $14$	Plug in the known values
$\text(Area)$ _{$\text(Rectangle)$}	$=$	$280 cm^2$

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

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

	$=$	$1/2 times$ $20$ $times$ $14$	Plug in the known values

$\text(Area)$ _{$\text(Triangle)$}	$=$	$140 cm^2$

Finally, get the final area by subtracting the area of the
Triangle from the area of the Rectangle

$\text{Total Area}$	$=$	$280$ $-$ $140$	Plug in the known values
	$=$	$140 cm^2$

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

$\text(Area)=140 cm^2$

Question 4 of 4

Find the area of the yellow-shaded region.

$\text(Area )=$ (54) $m^2$

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Area of a Triangle Formula

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

$times$ $\text(height)$

Area of a Square Formula

$\text(Area )=$ $\text(side)$

$times$ $\text(side)$

In a regular square, all sides are equal

Identify the known lengths

$\text(base)=15$

$\text(height)=18$

$\text(side)=9$

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

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

	$=$	$1/2 times$ $15$ $times$ $18$	Plug in the known values

$\text(Area)$ _{$\text(Triangle)$}	$=$	$135 m^2$

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

$\text(Area)$ _{$\text(Square)$}	$=$	$\text(side)$ $times$ $\text(side)$	Area of a Square Formula
	$=$	$9$ $times$ $9$	Plug in the known values
$\text(Area)$ _{$\text(Square)$}	$=$	$81 m^2$

Finally, get the final area by subtracting the area of the
Square from the area of the Triangle

$\text{Total Area}$	$=$	$135$ $-$ $81$	Plug in the known values
	$=$	$54 m^2$

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

$\text(Area)=54 m^2$

Areas of a Shaded Region

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Quiz summary

Information

1. Question

Hint

Great Work!

Area of a Square Formula

Identify the known lengths

2. Question

Hint

Correct!

Area of a Rectangle Formula

Identify the known lengths

3. Question

Hint

Keep Going!

Area of a Rectangle Formula

Area of a Triangle Formula

Identify the known lengths

4. Question

Hint

Fantastic!

Area of a Triangle Formula

Area of a Square Formula

Identify the known lengths

Quizzes