Areas of a Shaded Region
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Question 1 of 4
1. Question
Find the area of the black-shaded region.
- `\text(Area )=` (120) `cm^2`
Hint
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Area of a Square Formula
`\text(Area )=\text(side) times \text(side)`In a regular square, all sides are equalIdentify 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
2. Question
Find the area of the pink-shaded region.
The given measurements are in metres- `\text(Area )=` (154) `m^2`
Hint
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Incorrect
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
3. Question
Find the area of the blue-shaded region.
- `\text(Area )=` (140) `cm^2`
Hint
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Incorrect
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
4. Question
Find the area of the yellow-shaded region.
- `\text(Area )=` (54) `m^2`
Hint
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Fantastic!
Incorrect
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 equalIdentify 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`