Areas of parallelograms, triangles and trapeziums · Usually met around P5
Area of a triangle
Base × height ÷ 2: halve the even one first.
How to do it
Method
Base × height ÷ 2: halve the even one first
Base 8, height 5: 8 ÷ 2 = 4, 4 × 5 = 20
Another way
Half a parallelogram
8 × 5 = 40, 40 ÷ 2 = 20
In full
A triangle's area = base × height ÷ 2. Why: two matching triangles fit together into a parallelogram with the same base and height, so a triangle is half of it. Base 8 cm, height 5 cm: 8 × 5 = 40, 40 ÷ 2 = 20 cm². Quicker: halve the even number first to keep the numbers small: 8 ÷ 2 = 4, 4 × 5 = 20, the same. In a right triangle, one short side is the base and the other is the height. An obtuse triangle's height can land outside it: it is still the square distance from the opposite corner to the base's line. Careful: don't forget the ÷ 2, and don't use a slanting side as the height. Triangles on the same base with their top corners on one line parallel to it have the same height, so the same area.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
What is the area of this triangle?
Show the answer and working
Answer: 70 cm²
Area = base × height ÷ 2 = 14 × 10 ÷ 2 = 70.
Example 2
A triangle has a base of 9 cm and a height of 19 cm. What is its area in cm²?
Show the answer and working
Answer: 85.5 cm²
9 × 19 ÷ 2 = 85.5 cm².
Example 3
A triangle with base 14 cm and height 9 cm has an area of 63 cm².
True or false?
Show the answer and working
Answer: True
14 × 9 ÷ 2 = 63 cm²: don't forget the ÷ 2.
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