How to find the area of a parallelogram
The area of a parallelogram is base times perpendicular height: A = b × h. With base 8 and height 5, A = 8 × 5 = 40 square units. A rectangle is just a parallelogram with right angles — see the rectangle area calculator.
The formula comes from cutting a right triangle off one end of the shape and sliding it to the other end, which turns the parallelogram into a rectangle of the same base and height without changing its area.
How to use this calculator
Enter the base and the height in the same unit. The height must be the perpendicular distance between the base and the opposite side — not the length of the slanted edge. For two unequal parallel sides use the trapezoid area calculator.
Using the slanted side by mistake always overstates the area, because that edge is longer than the true height. Either side pair can serve as the base, as long as the height is measured perpendicular to that same side.
Worked example
A parallelogram sign has an 8-inch base and stands 5 inches tall (perpendicular). Area = 8 × 5 = 40 square inches.
To check the result, picture an 8 by 5 rectangle — the parallelogram covers exactly the same amount of surface, which is why leaning the shape over changes its outline but not its area. For the fence around the shape rather than the ground inside it, use the perimeter calculator.
Frequently asked questions
- What is the formula for the area of a parallelogram?
- A = base × height, using the perpendicular height between the base and the opposite side.
- What is the area of a parallelogram with base 8 and height 5?
- 40 square units (8 × 5).
- Do I use the slanted side as the height?
- No. Use the perpendicular (straight-up) height, which is shorter than the slanted side.
- What units is the area in?
- Square units of whatever you measured the base and height in.
- What if I only know the two sides and the angle between them?
- Then the area is a × b × sin(θ), where θ is the angle between the sides. That formula works because b × sin(θ) is exactly the perpendicular height, so it reduces to base × height.