Area of a Parallelogram — Formula & Examples

To find the area of a parallelogram, multiply the base by the perpendicular height. If the base is $b$ and the matching height is $h$, then

$$A = bh$$

The key word is perpendicular. The height is the shortest distance straight up from the base to the opposite side. It is not usually the slanted side length.

Why Base Times Height Works

Imagine cutting a right triangle from one side of the parallelogram and sliding it to the other side. The shape turns into a rectangle, but no area is lost or added.

A rectangle with the same base $b$ and height $h$ has area $bh$, so the parallelogram must also have area

$$A = bh$$

Area Of A Parallelogram Example

Suppose a parallelogram has base $8$ cm and perpendicular height $5$ cm. Substitute those values into the formula:

$$A = bh = 8 \times 5 = 40$$

So the area is $40\text{ cm}^2$.

If the slanted side happened to be $6$ cm, the answer would still be the same. Area depends on the base and the perpendicular height, not on the slanted edge by itself.

Common Mistakes With Parallelogram Area

Using The Slanted Side Instead Of The Height

This is the mistake that causes most wrong answers. If the diagram shows a slanted side and also shows a perpendicular height, use the perpendicular height for $h$.

For example, if $b = 8$, the slanted side is $6$, and the perpendicular height is $5$, then the correct area is still

$$8 \times 5 = 40$$

not $8 \times 6$.

Mixing Up Area And Perimeter

Area measures square units inside the shape. Perimeter measures the total distance around the outside. The numbers in the diagram may be the same, but the formulas answer different questions.

Forgetting Units

If lengths are in centimeters, the area should be written in square centimeters: $\text{cm}^2$.

When To Use This Formula

Use $A = bh$ whenever you know a base and the perpendicular height to that base. This is the standard formula in basic geometry, and it also helps explain why triangle area is $\frac{1}{2}bh$.

If you do not know the height, but you do know two adjacent sides $a$ and $b$ and the included angle $\theta$, you can write the area as

$$A = ab \sin \theta$$

because the height relative to side $b$ is $a \sin \theta$. This only works when $\theta$ is the included angle between those sides.

Try A Similar Problem

Find the area of a parallelogram with base $12$ m and perpendicular height $7$ m. Then change only the slanted side length and check that the area stays the same. That is a good way to test whether the idea of perpendicular height really clicks.