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5.10: Area of a Parallelogram

Last updated

Nov 28, 2020
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- 5.9: Parallelograms
- 5.11: Unknown Dimensions of Parallelograms

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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 $\PageIndex{6}$
Figure $\PageIndex{7}$
Figure $\PageIndex{8}$
Figure $\PageIndex{9}$
Figure $\PageIndex{10}$
Figure $\PageIndex{11}$
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

Review

Vocabulary

Additional Resources

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