Area of a Parallelogram

The space inside a parallelogram equals its base multiplied by its straight-up height.

A = b h

The base b runs along the bottom. The height h is measured straight up, not along the slanted edge.

What each symbol means

A: the area (the amount of space inside the shape)
b: the base (the length of one side you measure along)
h: the height (the straight-up distance to the opposite side, not the slanted side)

A parallelogram is a four-sided shape where opposite sides are parallel and the same length. It looks like a rectangle that has been pushed over to one side. To find how much space fits inside, you only need two measurements: the base and the height.

The formula is A = bh. In plain words: multiply the base by the height.

What each part means

The base is just the length of one side, usually the bottom one. The height is the tricky part. It is the straight-up distance from the base to the side across from it, measured at a right angle. It is not the length of the slanted side.

Do not use the slanted side: The most common mistake is to multiply the base by the slanted edge. The height must be the perpendicular distance (straight up), which is always shorter than the slant.

A worked example

Find the area of a parallelogram with base 8 cm and height 5 cm

Start with the formula: A = bh.
Put in the base and height: A = 8 × 5.
Multiply: A = 40.
The area is 40 square centimeters.

It is the rectangle formula in disguise: A rectangle is just a parallelogram with square corners. Both use base times height, because you can always cut a parallelogram into a rectangle of the same size.

A second example

A parallelogram-shaped garden has a base of 12 m and a height of 7 m. What is its area?

Use the formula: A = bh.
Put in the numbers: A = 12 × 7.
Multiply: A = 84.
The garden covers 84 square meters.

The area of a parallelogram is A = bh.
The height must be the straight-up (perpendicular) distance, not the slanted side.
It is the same rule as a rectangle, because you can reshape one into the other.
Area is always measured in square units.

Why it works (cut and slide into a rectangle)

Draw a parallelogram sitting on its base.
Cut straight down from the top corner to the base. This slices off a right triangle from one end.
Slide that triangle over to the other end, where it fits perfectly against the slanted side.
What you have left is a rectangle. Its width is the base b and its height is the same height h as before.
A rectangle has area width times height, which is b × h. Nothing was added or removed, so the parallelogram had that same area all along: A = bh.

Practice questions

Question 1

Find the area of a parallelogram with base 10 cm and height 4 cm.

Write the formula: A = bh.
Substitute the base b = 10 and the height h = 4: A = 10 × 4.
Multiply: A = 40.
Attach the units. Area is a surface, so it is measured in square cm.

Answer: 40 square cm

Question 2

A parallelogram has a base of 6 m and a height of 9 m. What is its area?

Start from A = bh.
Substitute b = 6 and h = 9: A = 6 × 9.
Multiply: A = 54.
The area is 54 square m.

Answer: 54 square m

Question 3

A parallelogram has base 7 cm, slanted side 6 cm, and height 5 cm. Find its area.

The formula needs the base and the height, not the slanted side.
The slanted side (6 cm) is a distractor here, so ignore it.
Use A = bh = 7 × 5.
Multiply: A = 35 square cm.

Answer: 35 square cm

Question 4

A parallelogram has an area of 48 square cm and a base of 8 cm. What is its height?

Start from A = bh, where A = 48 and b = 8.
This gives 48 = 8 × h.
To find the height, divide both sides by 8: h = 48 ÷ 8.
Work it out: h = 6 cm.

Answer: 6 cm

Question 5

Find the area of a parallelogram with base 2.5 m and height 4 m.

Use the formula A = bh.
Substitute b = 2.5 and h = 4: A = 2.5 × 4.
Multiply: 2.5 × 4 = 10.
The area is 10 square m.

Answer: 10 square m