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10.2: Area of a Parallelogram

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What if you wanted to find the area of a parallelogram? How does the area of a parallelogram relate to the area of a rectangle? After completing this Concept, you'll be able to solve problems like these.

Watch This

CK-12 Foundation: Chapter10AreaofaParallelogramA

Learn more about the area of parallelograms by watching the video at this link.

Guidance

Recall that a parallelogram is a quadrilateral whose opposite sides are parallel.

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

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 . Be careful! The height of a parallelogram is always perpendicular to the base. This means that the sides are not the height.

Example A

Find the area of the parallelogram.

A=15 \cdot 8=120 \ in^2

Example B

If the area of a parallelogram is 56 \ units^2 and the base is 4 units, what is the height?

Plug in what we know to the area formula and solve for the height.

56 &= 4h\\14 &= h

Example C

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

Solve for the base in A=bh .

60 \ units &= 12b\\5 \ units &= b

Watch this video for help with the Examples above.

CK-12 Foundation: Chapter10AreaofaParallelogramB

Vocabulary

Perimeter is 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.” Area is the amount of space inside a figure. Area is measured in square units. A parallelogram is a quadrilateral whose opposite sides are parallel.

Guided Practice

Find the area of the following shapes.

1.

2.

3. A parallelogram with a base of 10 m and a height of 12 m.

Answers:

1. Area is 15(6)=90 \ un^2 .

2. Area is 32(12)=672 \ un^2 .

3. Area is 10(12)=120 \ m^2 .

Interactive Practice

Practice

  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.

  1. If the area of a parallelogram is 42 \ units^2 and the base is 6 units, what is the height?
  2. If the area of a parallelogram is 48 \ units^2 and the height is 6 units, what is the base?
  3. If the base of a parallelogram is 9 units and the area is 108 \ units^2 , what is the height?
  4. If the height of a parallelogram is 11 units and the area is 27.5 \ units^2 , what is the base?

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Difficulty Level:

At Grade

Grades:

Date Created:

Jul 17, 2012

Last Modified:

Aug 21, 2014
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