Area of parallelograms
Theory
The area of a parallelogram is its base multiplied by its perpendicular height: \(A = b \times h\). The height is measured at a right angle to the base, not along the slanted side.
A parallelogram has two pairs of parallel sides. Its area is the space inside it.
The area is the base times the perpendicular height: \(A = b \times h\). The perpendicular height is the straight-line distance between the base and the opposite side.
Cutting a right-angled triangle from one end and sliding it to the other makes a rectangle \(b\) by \(h\), so the areas match.
| Base | Height | Area |
|---|---|---|
| \(9\) cm | \(5\) cm | \(45\) cm\(^2\) |
| \(12\) cm | \(7\) cm | \(84\) cm\(^2\) |
How to find the area of a parallelogram
- Identify the base and the perpendicular height (the one at a right angle to the base).
- Multiply base by height.
- Write the answer in square units.
| \(A\) | \(=\) | \(9 \times 5 = 45\) |
Area \(= 45\) cm\(^2\).
| \(A\) | \(=\) | \(12 \times 7 = 84\) |
Area \(= 84\) cm\(^2\).
Use the height \(5\), not the slant \(6\).
| \(A\) | \(=\) | \(8 \times 5 = 40\) |
Area \(= 40\) cm\(^2\).
| \(h\) | \(=\) | \(48 \div 8 = 6\) |
Height \(= 6\) cm.
Common pitfalls
Frequently asked questions
What is the area of a parallelogram?
Base times perpendicular height, \(A = b \times h\). A base of \(9\) and height of \(5\) give \(45\) square units.
Why is it base times height?
Cutting a triangle off one end and sliding it to the other turns the parallelogram into a rectangle \(b\) by \(h\) with the same area.
Which measurement is the height?
The perpendicular height — the straight-line distance between the base and the opposite side, meeting the base at a right angle.
What units is the area in?
Square units. A base and height in centimetres give an area in square centimetres.