Cut the triangle off one end of a parallelogram and slide it to the other end: you get a rectangle with the same base and height. So the area of a parallelogram is base × height. The height is the perpendicular height, at right angles to the base, not the slanted side. There is no ½, because a parallelogram is two whole triangles. If you know the area and one length, divide to find the other: height = area ÷ base.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- parallelogram
- a four-sided shape with two pairs of parallel sides
- perpendicular height
- the distance between the parallel sides, measured at a right angle
Worked examples
A parallelogram has a base of 9 cm and a height of 4 cm. What is its area?
- 1.Area = base × height.
- 2.9 × 4 = 36 cm².
= 36
A parallelogram has a base of 10 cm, a height of 4 cm and a slanted side of 5 cm. What is its area?
- 1.Use the perpendicular height, not the slanted side.
- 2.10 × 4 = 40 cm².
= 40
A parallelogram has an area of 48 cm² and a base of 8 cm. What is its height?
- 1.48 = 8 × height.
- 2.height = 48 ÷ 8 = 6 cm.
= 6
For parents
Method: Rearrange into a rectangle
What to say: Which line is at right angles to the base? Can you turn the shape into a rectangle?
Common mistakes:
- Multiplies the base by the slanted side instead of the perpendicular height.
- Uses the triangle rule and halves base × height.
- Adds the base and height instead of multiplying.
- Finds a missing base or height with the triangle rule, so the answer is twice too big.
- Subtracts the known length from the area instead of dividing.
- Treats the labelled slanted side as the perpendicular height.