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5.10: Area of a Parallelogram

  • Page ID
    4994
  • Use \(A=bh\) to find area.

    A parallelogram is a quadrilateral whose opposite sides are parallel.

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    Figure \(\PageIndex{1}\)

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

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    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.

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    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.

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    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

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

    Find the area of the parallelogram.

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      Figure \(\PageIndex{6}\)
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      Figure \(\PageIndex{7}\)
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      Figure \(\PageIndex{8}\)
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      Figure \(\PageIndex{9}\)
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      Figure \(\PageIndex{10}\)
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      Figure \(\PageIndex{11}\)
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      Figure \(\PageIndex{12}\)
    8. If the area of a parallelogram is \(42\text{ units }^2\) and the base is \(6\text{ units }\), what is the height?
    9. If the area of a parallelogram is \(48\text{ units }^2\) and the height is \(6\text{ units }\), what is the base?
    10. If the base of a parallelogram is 9 units and the area is \(108\text{ units }^2\), what is the height?
    11. 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