Question

Find the area of this shape in two different ways.

Answer 1

10 meters²

Explanation:

Method 1 ~

This method adds the triangle with the two rectangles.

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First find the area of the largest rectangle ~

Width = 4 meters - 2 meters = 2 meters

Length = 3 meters

Area = Width × Length = 2 meters × 3 meters = 6 meters²

Then find the area of the second rectangle ~

Width = 1 meter

Length = 2 meters

Area = Width × Length = 1 meter × 2 meters = 2 meters²

Then find the area of the triangle ~

Base = 3 meters - 1 meter = 2 meters

Height = 2 meters

Area =
`(bh)/(2)` =
`(2*2)/(2)` =
`(4)/(2)` = 2 meters²

Finally, add the triangle and the two rectangles together ~

6 meters² + 2 meters² + 2 meters² = 10 meters²

Method 2 ~

This method subtracts the triangle from the whole rectangle.

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First find the area of the rectangle ~

Width = 3 meters

Length = 4 meters

Area = Width × Length = 3 meters × 4 meters = 12 meters²

Then find the area of the triangle ~

Base = 3 meters - 1 meter = 2 meters

Height = 2 meters

Area =
`(bh)/(2)` =
`(2*2)/(2)` =
`(4)/(2)` = 2 meters²

Lastly, subtract the triangle with the rectangle ~

12 meters² - 2 meters² = 10 meters²