Maths Library

Area of Triangles and Parallelograms: Year 7 maths

This topic covers calculating the area of triangles, parallelograms, and related composite polygons. Students practise selecting the correct perpendicular height, applying standard area formulae, and rearranging to find unknown sides.

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What this covers

Area of Triangles and Parallelograms is taught in Year 7 (age 11 to 12, KS3) as a main teaching focus. It sits in the Measurement strand.

Worked example

Calculate the area of a triangle with base 12 cm and perpendicular height 7 cm.

  1. Use the formula for the area of a triangle: Area = (base × height) ÷ 2.
  2. Multiply base and height: 12 × 7 = 84.
  3. Divide by 2: 842 = 42 cm^2.

Answer: 42 cm^2

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Right-angled triangles with integer base and height given.
  2. General triangles and parallelograms where perpendicular height is explicitly marked.
  3. Shapes with distractor measurements (e.g. slant heights provided alongside perpendicular height).
  4. Triangles and parallelograms involving decimals or fractions.
  5. Composite shapes combining triangles and parallelograms, or solving for missing height given area.

Common mistakes

  • Using the slanted side length instead of the vertical perpendicular height.
  • Forgetting to divide by 2 when calculating the area of a triangle.

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Calculate perimeters and areas of composite shapes, triangles, parallelograms, and trapezia.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Area of Triangles and Parallelograms

Year 7 maths

Qs
6
Marks
18
NameDateScore / 18
1.
Find the area of a parallelogram with base 11 cm and perpendicular height 6 cm.
[3]
2.
Find the area of a triangle with base 8 cm and perpendicular height 5 cm.
8 cm
[3]
3.
Find the area of a parallelogram with base 12 cm and perpendicular height 7 cm.
[3]
4.
Find the area of a parallelogram with base 8 cm and perpendicular height 9 cm.
[3]
5.
Find the area of a triangle with base 9 cm and perpendicular height 8 cm.
9 cm
[3]
6.
Find the area of a triangle with base 8 cm and perpendicular height 10 cm.
8 cm
[3]

Answer key

  1. 66 cm2Area = base × perpendicular height; 11 × 6 = 66 cm2
  2. 20 cm2Area = base × height ÷ 2; 8 × 5 ÷ 2 = 20 cm2
  3. 84 cm2Area = base × perpendicular height; 12 × 7 = 84 cm2
  4. 72 cm2Area = base × perpendicular height; 8 × 9 = 72 cm2
  5. 36 cm2Area = base × height ÷ 2; 9 × 8 ÷ 2 = 36 cm2
  6. 40 cm2Area = base × height ÷ 2; 8 × 10 ÷ 2 = 40 cm2