Area of Parallelograms Examples: 24 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Area of Parallelograms.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The area of a parallelogram is the product of its base and perpendicular height: $A = bh$ .

Cut a triangle off one end of the parallelogram and slide it to the other end — you get a rectangle with the same base and height.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A parallelogram's area is base times perpendicular height, because cutting a triangle off one end and sliding it to the other makes a rectangle of the same base and height.

Common stuck point: The procedure for area of parallelograms is the easy part; the trap is using the slanted side as the height. Asking "Is the height I am using the perpendicular distance between the parallel bases, not the slanted side?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Is the height I am using the perpendicular distance between the parallel bases, not the slanted side?

Worked Examples

Example 1

medium

A parallelogram has base

14

and height

5

. If both are doubled, find the new area.

Answer

280

First step

Original area

=14\times 5=70

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Example 2

medium

A parallelogram has sides

8

and

10

with included angle

60°

. Find its area.

Example 3

medium

A parallelogram-shaped tile has base

20

cm and slant side

13

cm. The height to the base is

12

cm. Find the tile's area.

Example 4

hard

A parallelogram has vertices

(0,0)

(4,0)

(6,5)

(2,5)

. Find its area.

Example 5

hard

A parallelogram has sides

a=5

b=7

with included angle

\theta

giving area

20

. Find

\sin\theta

Example 6

hard

A parallelogram has vectors

\vec u=(3,1)

\vec v=(1,4)

for its sides. Find its area.

Example 7

hard

A parallelogram is inscribed in a rectangle that is

14

9

, sharing two opposite vertices. The parallelogram's area is what fraction of the rectangle's?

Example 8

hard

A parallelogram has vertices

(0,0)

(6,2)

(8,7)

(2,5)

. Find its area using the cross-product method.

Example 9

challenge

A rhombus has perimeter

52

and one diagonal

24

. Find its area.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Find the area of a parallelogram with base

5

and height

9

Example 2

easy

Find the area of a parallelogram with base

12

and height

3

Example 3

easy

A parallelogram has sides 6 and 10 and a perpendicular height of 4 to the side of length 10. Find the area.

Example 4

easy

Why can't the slanted side of a parallelogram be used as the height?

Example 5

easy

What units does the area of a parallelogram have if the base and height are in cm?

Example 6

medium

A parallelogram has vertices

(0,0)

(7,0)

(10,4)

(3,4)

. Find its area.

Example 7

medium

A rhombus has diagonals

10

and

12

. Find its area.

Example 8

medium

A parallelogram has area

144

cm². If its base is

18

cm, find its height.

Example 9

medium

Two parallelograms share a base of

12

. One has height

5

, the other has height

8

. How much larger is the second area?

Example 10

medium

A parallelogram has base

b

, height

h

, area

48

. If a new parallelogram has base

2b

and height

\tfrac{h}{2}

, find its area.

Example 11

hard

A rhombus has side

13

and one diagonal

10

. Find its area.

Example 12

hard

A parallelogram has area

60

. A new parallelogram is formed by tripling the base only. Find its area.

Example 13

hard

A parallelogram has area

80

m². If only the height doubles, find the new area.

Example 14

hard

A parallelogram-shaped parking spot is

2.5

m by

5

m with a perpendicular height of

2

m to the

5

-m base. Find its area.

Example 15

challenge

A parallelogram and a triangle with the same base have equal areas. If the parallelogram's height is

h

, what is the triangle's height?

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Related Concepts

Area Basic Shapes Area of Triangles Area of Trapezoids

Background Knowledge

These ideas may be useful before you work through the harder examples.

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