Areas of a Shaded Region

Question 1 of 4

Find the area of the black-shaded region.

$Area =$ $\text(Area )=$ (120) $c m^{2}$ $cm^2$

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Area of a Square Formula

Area = side \times side

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

In a regular square, all sides are equal

Identify the known lengths

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

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

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

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

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

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

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

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

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

Area = 120 c m^{2}

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

Question 2 of 4

Find the area of the pink-shaded region.

The given measurements are in metres

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

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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) $= 17$ $=17$

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

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

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

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

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

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

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

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

Area = 154 m^{2}

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

Question 3 of 4

Find the area of the blue-shaded region.

$Area =$ $\text(Area )=$ (140) $c m^{2}$ $cm^2$

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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

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

\times

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

Identify the known lengths

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

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

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

$Area$ $\text(Area)$ _{$Rectangle$ $\text(Rectangle)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $width$ $\text(width)$	Area of a Rectangle Formula
	$=$ $=$	$20$ $20$ $\times$ $times$ $14$ $14$	Plug in the known values
$Area$ $\text(Area)$ _{$Rectangle$ $\text(Rectangle)$}	$=$ $=$	$280 c m^{2}$ $280 cm^2$

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

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

	$=$ $=$	$\frac{1}{2} \times$ $1/2 times$ $20$ $20$ $\times$ $times$ $14$ $14$	Plug in the known values

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

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

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

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

Area = 140 c m^{2}

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

Question 4 of 4

Find the area of the yellow-shaded region.

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

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Area of a Triangle Formula

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

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

\times

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

Area of a Square Formula

Area =

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

\times

$times$ $side$ $\text(side)$

In a regular square, all sides are equal

Identify the known lengths

$base = 15$ $\text(base)=15$

$height = 18$ $\text(height)=18$

$side = 9$ $\text(side)=9$

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

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

	$=$ $=$	$\frac{1}{2} \times$ $1/2 times$ $15$ $15$ $\times$ $times$ $18$ $18$	Plug in the known values

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

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

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

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

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

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

Area = 54 m^{2}

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

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