Areas of parallelograms, triangles and trapeziums · Usually met around P5
Area of a parallelogram
Base × height: the slanting side isn't the height.
How to do it
Method
Base × height: the slanting side isn't the height
Base 8, height 5: 8 × 5 = 40
Another way
Cut and move into a rectangle
An 8 by 5 rectangle: 8 × 5 = 40
In full
A parallelogram's area = base × height. Why: cut the triangle off one end along the height and move it to the other end, and you have a rectangle as long as the base and as wide as the height, with the same area. Base 8 cm, height 5 cm: 8 × 5 = 40 cm². Careful: the slanting side is not the height; the height is square to the base. So a parallelogram and a rectangle with the same base and height have the same area, however long the slanting side. Another way to see it: cut along a diagonal into two matching triangles, each 8 × 5 ÷ 2 = 20, and 20 + 20 = 40, the same.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A parallelogram has a base of 18 cm and a height of 18 cm. What is its area in cm²?
Show the answer and working
Answer: 324 cm²
18 × 18 = 324 cm².
Example 2
A parallelogram has base 14 cm, height 9 cm and slanting sides 10 cm. Cut the triangle off one end along the height and move it to the other end to make a rectangle. How long and how wide is the rectangle?
- A. 28 cm long, 9 cm wide
- B. 10 cm long, 9 cm wide
- C. 14 cm long, 9 cm wide
- D. 14 cm long, 10 cm wide
Choose the right answer
Show the answer and working
Answer: C. 14 cm long, 9 cm wide
After the move it is the base 14 long and the height 9 wide, with the same area: 14 × 9.
Example 3
A parallelogram has a base of 8.5 m and a height of 2 m. What is its area in m²?
Show the answer and working
Answer: 17 m²
8.5 × 2 = 17 m².
Practise it in the game →Areas of parallelograms, triangles and trapeziums · Free to start, unlimited questions, no download