Practice Area of triangles, parallelograms and trapezoids
A triangle has area equal to half its base times its perpendicular height.
The height must correspond to the chosen base, even when it lies outside the triangle.
Exercises with solutions
The area of a triangle is A = (base · height) ÷ 2. The height is always perpendicular to the base. For a parallelogram A = base · height, and for a trapezium A = (a + c) ÷ 2 · height.
Exercise 1
A triangle has base 8 cm and height 5 cm. Calculate the area.
Show solution and working
20 cm²
A = (8 cm · 5 cm) ÷ 2 = 40 cm² ÷ 2 = 20 cm².
Exercise 2
Why do you divide by 2 for a triangle?
Show solution and working
because a triangle is half a parallelogram
Two identical triangles together form a parallelogram of area base · height. So a triangle is half that size.
Exercise 3
A triangle has base 10 cm and area 35 cm². How large is the height?
Show solution and working
7 cm
From A = (base · height) ÷ 2 it follows that h = 2 · A ÷ base = 70 cm² ÷ 10 cm = 7 cm.
Exercise 4
A parallelogram has base 6 cm and height 4 cm. Calculate the area.
Show solution and working
24 cm²
For a parallelogram you do not halve: A = 6 cm · 4 cm = 24 cm².
Common mistake
Forgetting to divide by 2 for a triangle, or wrongly halving a parallelogram. And using a slanted side as the height: the height is always perpendicular to the base.
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