Areas of parallelograms, triangles and trapeziums · Usually met around P5
Area of a trapezium
(top + bottom) × height ÷ 2.
How to do it
Method
(top + bottom) × height ÷ 2
Top 3, bottom 7, height 4: 10 × 4 ÷ 2 = 20
Another way
Two triangles
3 × 4 ÷ 2 + 7 × 4 ÷ 2 = 6 + 14 = 20
In full
A trapezium's area = (top + bottom) × height ÷ 2. Why: two matching trapeziums, one turned upside down, fit together into a parallelogram whose base is top + bottom and whose height is the same, so a trapezium is half of it. Top 3 cm, bottom 7 cm, height 4 cm: 3 + 7 = 10, 10 × 4 = 40, 40 ÷ 2 = 20 cm². Another way: cut along a diagonal into two triangles, 3 × 4 ÷ 2 + 7 × 4 ÷ 2 = 6 + 14 = 20, the same. Or cut it into a rectangle in the middle and triangles at the ends, and add. Careful: add the two parallel sides, don't multiply them; don't forget the ÷ 2; a slanting side isn't the height.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A trapezium's top and bottom add up to 19 cm, and its height is 6 cm. What is its area in cm²?
Show the answer and working
Answer: 57 cm²
The formula only needs top + bottom: 19 × 6 ÷ 2 = 57; you don't need each one.
Example 2
A trapezium's top is 7 cm, its bottom 8 cm and its height 12 cm. What is its area in cm²?
Show the answer and working
Answer: 90 cm²
(7 + 8) × 12 ÷ 2 = 90 cm².
Example 3
A trapezium with top 5 cm, bottom 17 cm and height 8 cm has an area of 340 cm².
True or false?
Show the answer and working
Answer: False
(5 + 17) × 8 ÷ 2 = 88 cm².
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