What is the difference between the area of a parallelogram and a rectangle?

A rectangle is a special parallelogram where all angles are 90°. Both use the formula A = bh, but in a rectangle, the height equals the width. An irregular parallelogram requires you to find or measure the perpendicular height separately from the side lengths.

Can I use any side as the base?

Yes. You can choose any side as the base, but the height must then be the perpendicular distance to the opposite parallel side. Different base choices give different height values, but the product bh always gives the same total area.

How do I find the height if I only have the side lengths?

If you know a side length and an angle, use h = \text{side} \times \sin(\text{angle}). Otherwise, construct or draw the parallelogram and use the Pythagorean Theorem on the right triangle formed by dropping a perpendicular from the top to the base.

Does the formula change for a slanted parallelogram?

No. The formula A = bh works for any parallelogram, no matter how slanted. The key is that h must be the perpendicular distance, not the side length. A very slanted parallelogram has a smaller height relative to its side length, giving it less area than a more upright one with the same base.

Area of a Parallelogram

Find the area of any parallelogram by multiplying its base by the perpendicular height—a formula that works even when sides aren't perpendicular.

A = bh

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What each symbol means

What Area of a Parallelogram takes

Symbol	Meaning
$A$	The area of the parallelogram, measured in square units such as $\text{cm}^2$ or $\text{m}^2$ ; if you read this as a side length or perimeter, you will get incorrect units.
$b$	The base—any one of the four sides chosen as the reference; always a length in linear units like centimeters or meters.
$h$	The perpendicular (vertical) distance from the base to the opposite parallel side, not the slant side length; confusing this with a side's actual length causes most errors.

When to use it

You need this when finding the area enclosed by a four-sided shape with opposite parallel sides.

Level

Usually taught in: Geometry

Worked examples

1. Find the area of a parallelogram with base 5 and height 3

Problem

A parallelogram has a base of 5 cm and a perpendicular height of 3 cm. What is its area?

$A = bh$
We write the area formula for a parallelogram.
$A = 5 \cdot 3$
We substitute the base $b = 5$ and height $h = 3$ into the formula.
$A = 15$
We multiply $5 \cdot 3 = 15$ .

Answer: $A = 15 \text{ cm}^2$

We apply the formula directly with the base and perpendicular height given. The answer is in square units because we multiply two lengths together to find area.

2. Find the area of a parallelogram with fractional dimensions

Problem

A parallelogram has a base of

\frac{12}{5}

feet and a perpendicular height of

\frac{5}{4}

feet. What is its area?

$A = bh$
We start with the area formula.
$A = \frac{12}{5} \cdot \frac{5}{4}$
We substitute $b = \frac{12}{5}$ and $h = \frac{5}{4}$ into the formula.
$A = \frac{12 \cdot 5}{5 \cdot 4}$
We multiply the numerators together and the denominators together.
$A = \frac{60}{20} = 3$
We simplify by canceling the 5s: $\frac{60}{20} = 3$ .

Answer: $A = 3 \text{ ft}^2$

Fractions multiply the same way as whole numbers. The key is to simplify after multiplying; here the common factor of 5 cancels from numerator and denominator, leaving a clean integer.

3. Find the area of a parallelogram laboratory work surface

Problem

A science laboratory has a parallelogram-shaped work surface that is 15 feet along its base and 6 feet in perpendicular height. The lab needs a protective covering. What is the area to be covered?

$b = 15 \text{ ft}, \quad h = 6 \text{ ft}$
We identify the base and perpendicular height from the problem.
$A = bh$
We write the area formula for a parallelogram.
$A = 15 \cdot 6$
We substitute the base and height values.
$A = 90$
We multiply $15 \cdot 6 = 90$ .

Answer: $A = 90 \text{ ft}^2$

In practical problems, measurements are given explicitly, and the base-times-height formula applies regardless of the parallelogram's angle. The lab needs enough covering for 90 square feet of work surface.

Common mistakes

Where Area of a Parallelogram usually goes wrong

The mistake	Why it is wrong	The fix
Writing $A = \text{side} \times \text{side}$ , multiplying two adjacent side lengths instead of base times perpendicular height.	In a slanted parallelogram, the two side lengths are not the base and height; the height is always perpendicular to the base.	Always identify the perpendicular distance from one parallel side to the other; measure or calculate this separately if only side lengths are given.
Using the slant side length as the height—for example, calculating $A = 10 \times 8$ when the base is 10, the slant side is 8, but the actual perpendicular height is only 6.	The slant side and the perpendicular height are different; using the wrong value gives an incorrect area that is too large.	Draw a right triangle formed by dropping a perpendicular from the top of the parallelogram to the base; use the Pythagorean Theorem if needed to find the true height.
Forgetting units or writing only $A = 48$ instead of $A = 48 \text{ m}^2$ .	Area always has square units; an answer without units is incomplete and meaningless.	Always write the unit as the square of the linear unit used for base and height, such as $\text{cm}^2$ , $\text{m}^2$ , or $\text{in}^2$ .

Tips and when to use something else

The height must be perpendicular to the base; if you are given a slant side instead, use the Pythagorean Theorem on the right triangle formed by the height and base.
A rectangle is a special parallelogram where the height equals the width, so the formula becomes length times width—a familiar formula you already know.
For a triangle, the area formula is $A = \frac{1}{2}bh$ , exactly half a parallelogram, because two identical triangles fit together to make a parallelogram.
You can choose any side as the base, but the height must always be the perpendicular distance to the opposite side; the product $bh$ gives the same area regardless of which side you pick as the base.

Related formulas

Area of a RectangleMultiply the length and width of a rectangle to find the total area of flat space it covers, measured in square units.Area of a TriangleCalculates the area enclosed by a triangle given its base and perpendicular height; essential for geometry, SAT, and ACT math problems involving triangles.Area of a TrapezoidCalculates the exact area of any trapezoid when you know the lengths of both parallel bases and the perpendicular height between them.

Frequently asked questions

What is the difference between the area of a parallelogram and a rectangle?: A rectangle is a special parallelogram where all angles are 90°. Both use the formula $A = bh$ , but in a rectangle, the height equals the width. An irregular parallelogram requires you to find or measure the perpendicular height separately from the side lengths.
Can I use any side as the base?: Yes. You can choose any side as the base, but the height must then be the perpendicular distance to the opposite parallel side. Different base choices give different height values, but the product $bh$ always gives the same total area.
How do I find the height if I only have the side lengths?: If you know a side length and an angle, use $h = \text{side} \times \sin(\text{angle})$ . Otherwise, construct or draw the parallelogram and use the Pythagorean Theorem on the right triangle formed by dropping a perpendicular from the top to the base.
Does the formula change for a slanted parallelogram?: No. The formula $A = bh$ works for any parallelogram, no matter how slanted. The key is that $h$ must be the perpendicular distance, not the side length. A very slanted parallelogram has a smaller height relative to its side length, giving it less area than a more upright one with the same base.

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Reviewed 2026-09-18