The idea, step by step
Area counts square units
A rectangle with length 7 cm and width 4 cm holds 7 rows of 4 square-centimetre tiles. Its area is 28 cm². A parallelogram can be cut and slid to make a rectangle without changing its area, so it also uses base × perpendicular height. The height must meet the base, or an extension of it, at a right angle.
A triangle is half a parallelogram
Two matching copies of any triangle can make a parallelogram. One triangle therefore has half the area of base × height. You may choose any side as the base, but must use the perpendicular height paired with that base. For a composite region, split it into non-overlapping simple shapes or subtract a missing rectangle.
A common trap
Using the sloping side as the height of a triangle or parallelogram.
Instead: Look for the line perpendicular to the chosen base. The height often lies inside the shape as a dashed line.
See the thinking
Triangle height, not the sloping side
A triangle has base 12 cm and perpendicular height 5 cm. Find its area.
- Use the perpendicular height marked by the right-angle symbol.
- Area = ½ × 12 × 5 = 30.
Parallelogram with extra information
A parallelogram has base 10 cm, perpendicular height 6 cm and sloping side 7 cm. Find its area.
- The sloping side is not the perpendicular height.
- Area = 10 × 6 = 60.
Check your understanding
Find the area of a triangle with base 8 m and perpendicular height 3 m.
Show answer
12 m²
½ × 8 × 3 = 12 m².
Your turn
6 questions · 13 marks · Work at your own pace.
Read the questions online
- Find the area of a rectangle 9 cm by 6 cm.1 mark
- Find the area of a triangle with base 14 cm and perpendicular height 5 cm.2 marks
- A parallelogram has base 11 m, perpendicular height 4 m and sloping side 5 m. Find its area.2 marks
- A triangle has area 36 cm² and base 12 cm. Find its perpendicular height.3 marks
- Find the area of the L-shaped region shown.3 marks
- A triangle and a parallelogram have the same base and perpendicular height. The parallelogram has area 48 cm². Find the triangle area and explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find the area of a rectangle 9 cm by 6 cm.1 mark
9 × 6 = 54 cm².
54 cm² - Find the area of a triangle with base 14 cm and perpendicular height 5 cm.2 marks
½ × 14 × 5 = 35 cm².
35 cm² - A parallelogram has base 11 m, perpendicular height 4 m and sloping side 5 m. Find its area.2 marks
Use height 4 m, not sloping side 5 m.
11 × 4 = 44 m².
44 m² - A triangle has area 36 cm² and base 12 cm. Find its perpendicular height.3 marks
36 = ½ × 12 × height.
36 = 6 × height.
Height = 36 ÷ 6 = 6 cm.
6 cm - Find the area of the L-shaped region shown.3 marks
Full rectangle: 9 × 7 = 63 m².
Missing rectangle: 4 × 3 = 12 m².
63 − 12 = 51 m².
51 m² - A triangle and a parallelogram have the same base and perpendicular height. The parallelogram has area 48 cm². Find the triangle area and explain.2 marks
A triangle has half the area for the same base and height.
48 ÷ 2 = 24 cm².
24 cm²
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 7 measurement and spatial representation: areas of triangles/parallelograms, prism volumes, circle circumference, nets and views. Precision is integrated into practical measurement; circle area is not introduced here.
Official curriculum source ↗