5.10: Area of a Parallelogram

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Use \(A=bh\) to find area.

A parallelogram is a quadrilateral whose opposite sides are parallel.

f-d_c058957aec562e4e5fe22a2699195b513b9ef4fe8103c68d6ee20c5d+IMAGE_TINY+IMAGE_TINY.png — Figure \(\PageIndex{1}\)

To find the area of a parallelogram, make it into a rectangle.

f-d_230440f0af3754bd1fb401b5b68a7be4dfc7bc97358f441862c2171f+IMAGE_TINY+IMAGE_TINY.png — Figure \(\PageIndex{2}\)

From this, we see that the area of a parallelogram is the same as the area of a rectangle. The area of a parallelogram is \(A=bh\). The height of a parallelogram is always perpendicular to the base. This means that the sides are not the height.

f-d_e5a6310e7a5ece578f1dbf95797b780865681898f45481c0778db61d+IMAGE_TINY+IMAGE_TINY.png — Figure \(\PageIndex{3}\)

What if you were given a parallelogram and the size of its base and height? How could you find the amount of space the parallelogram takes up?

Example \(\PageIndex{1}\)

Find the area of the parallelogram.

f-d_124d1912ef31cfddbd02db40621e4aca157d49991cdb9a6efa69687c+IMAGE_TINY+IMAGE_TINY.png — Figure \(\PageIndex{4}\)

Solution

Area is \(15(6)=90\text{ un}^2\).

Example \(\PageIndex{2}\)

Find the area of the parallelogram with a base of 10 m and a height of 12 m.

Solution

Area is 10(12)=120\text{ m}^2\).

Example \(\PageIndex{3}\)

Find the area of the parallelogram.

f-d_6823e5aa0dde3127aa73a6185e89891adea9514113ae48f6cfe82e55+IMAGE_TINY+IMAGE_TINY.png — Figure \(\PageIndex{5}\)

Solution

\(A=15\cdot 8=120 \text{ in}^2\)

Example \(\PageIndex{4}\)

If the area of a parallelogram is \(56 \text{ units }^2\) and the base is 4 units, what is the height?

Solution

Solve for the height in \(A=bh\).

\(56\text{ units }=4h\)

\(14 \text{ units }=h\)

Example \(\PageIndex{5}\)

If the height of a parallelogram is 12 m and the area is \(60 m^2\), how wide is the base?

Solution

Solve for the base in \(A=bh\).

\(60 \text{ units } =12b\)

\(5 \text{ units } =b\)

Review

Find the area of a parallelogram with height of 20 m and base of 18 m.
Find the area of a parallelogram with height of 12 m and base of 15 m.
Find the area of a parallelogram with height of 40 m and base of 33 m.
Find the area of a parallelogram with height of 32 m and base of 21 m.
Find the area of a parallelogram with height of 25 m and base of 10 m.

Find the area of the parallelogram.

Figure \(\PageIndex{6}\)
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Figure \(\PageIndex{12}\)
If the area of a parallelogram is \(42\text{ units }^2\) and the base is \(6\text{ units }\), what is the height?
If the area of a parallelogram is \(48\text{ units }^2\) and the height is \(6\text{ units }\), what is the base?
If the base of a parallelogram is 9 units and the area is \(108\text{ units }^2\), what is the height?
If the height of a parallelogram is 11 units and the area is \(27.5\text{ units }^2\), what is the base?

Vocabulary

Term	Definition
area	The amount of space inside a figure. Area is measured in square units.
perimeter	The distance around a shape. The perimeter of any figure must have a unit of measurement attached to it. If no specific units are given (feet, inches, centimeters, etc), write *units.*
Parallelogram	A parallelogram is a quadrilateral with two pairs of parallel sides.
Area of a Parallelogram	The area of a parallelogram is equal to the base multiplied by the height: \(A = bh\). The height of a parallelogram is always perpendicular to the base (the sides are not the height).

Additional Resources

Interactive Element

Video: Area of a Parallelogram (Whole Numbers)

Activities: Area of a Parallelogram Discussion Questions

Study Aids: Triangles and Quadrilaterals Study Guide

Practice: Area of a Parallelogram

Real World: Perimeter