Area of Parallelograms Examples in Math

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=bhA = 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.

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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 1414 and height 55. If both are doubled, find the new area.

Answer

280

First step

1
Original area =14×5=70=14\times 5=70.

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Example 2

medium
A parallelogram has sides 88 and 1010 with included angle 60°60°. Find its area.

Example 3

medium
A parallelogram-shaped tile has base 2020 cm and slant side 1313 cm. The height to the base is 1212 cm. Find the tile's area.

Example 4

hard
A parallelogram has vertices (0,0)(0,0), (4,0)(4,0), (6,5)(6,5), (2,5)(2,5). Find its area.

Example 5

hard
A parallelogram has sides a=5a=5, b=7b=7 with included angle θ\theta giving area 2020. Find sin⁡θ\sin\theta.

Example 6

hard
A parallelogram has vectors u⃗=(3,1)\vec u=(3,1), v⃗=(1,4)\vec v=(1,4) for its sides. Find its area.

Example 7

hard
A parallelogram is inscribed in a rectangle that is 1414 by 99, sharing two opposite vertices. The parallelogram's area is what fraction of the rectangle's?

Example 8

hard
A parallelogram has vertices (0,0)(0,0), (6,2)(6,2), (8,7)(8,7), (2,5)(2,5). Find its area using the cross-product method.

Example 9

challenge
A rhombus has perimeter 5252 and one diagonal 2424. 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 55 and height 99.

Example 2

easy
Find the area of a parallelogram with base 1212 and height 33.

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)(0,0), (7,0)(7,0), (10,4)(10,4), (3,4)(3,4). Find its area.

Example 7

medium
A rhombus has diagonals 1010 and 1212. Find its area.

Example 8

medium
A parallelogram has area 144144 cm². If its base is 1818 cm, find its height.

Example 9

medium
Two parallelograms share a base of 1212. One has height 55, the other has height 88. How much larger is the second area?

Example 10

medium
A parallelogram has base bb, height hh, area 4848. If a new parallelogram has base 2b2b and height h2\tfrac{h}{2}, find its area.

Example 11

hard
A rhombus has side 1313 and one diagonal 1010. Find its area.

Example 12

hard
A parallelogram has area 6060. A new parallelogram is formed by tripling the base only. Find its area.

Example 13

hard
A parallelogram has area 8080 m². If only the height doubles, find the new area.

Example 14

hard
A parallelogram-shaped parking spot is 2.52.5 m by 55 m with a perpendicular height of 22 m to the 55-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 hh, what is the triangle's height?
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Background Knowledge

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

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