GCSE MATHS • HIGHER TIER
Area of Triangles Made Simple
Learn how to calculate the area of triangles, identify the correct perpendicular height, rearrange the formula to find missing measurements and solve GCSE exam-style problems.
Clear method
Exam practice
Worked proofs
Area of Triangles in Four Moves
1
Identify
Identify the base and the perpendicular height of the triangle.
2
Formula
Area = ½ × base × height
3
Substitute
Substitute the base and perpendicular height into the formula.
4
Conclude
Multiply the values and divide by 2, then give the answer in square units.
What You’ll Learn
Understand Area
Understand that area measures the amount of space inside a two-dimensional shape and is measured in square units.
Use the Triangle Formula
Calculate the area of a triangle using Area = ½ × base × height.
Identify the Correct Height
Recognise that the height must be perpendicular to the chosen base.
Find Missing Measurements
Rearrange the area formula to calculate a missing base or height.
Key Rules
Use the correct formula
Area = ½ × base × height
Use the perpendicular height
The height must meet the base at a right angle (90°).
Remember to divide by 2
A triangle is half of a parallelogram with the same base and perpendicular height.
Use square units
Area should be written in units such as cm², m² or mm².
Worked Proof: Finding the Area
1. Identify
Base = 8 cm
Height = 5 cm
2. Formula
Area = ½ × base × height
3. Substitute
Area = ½ × 8 × 5
4. Calculate
Area = 20 cm²
More Worked Examples
1
Basic Area
Question: A triangle has a base of 12 cm and a height of 7 cm.
Area = ½ × 12 × 7
Area = 42 cm²
Area = 42 cm²
2
Decimal Area
Question: A triangle has a base of 15 cm and a height of 9 cm.
Area = ½ × 15 × 9
Area = 67.5 cm².
Area = 67.5 cm².
3
Finding the Height
Question: The area of a triangle is 30 cm² and its base is 10 cm. Find the height.
30 = ½ × 10 × h
30 = 5h
h = 6 cm
30 = 5h
h = 6 cm
4
Larger Triangle
Question: A triangle has a base of 20 cm and a height of 11 cm.
Area = ½ × 20 × 11.
Area = 110 cm²
Area = 110 cm²
- Common GCSE Mistakes
- Forgetting ÷ 2: Always halve the product of the base and height.
- Wrong height: Use the perpendicular height, not a sloping side.
- Wrong units: Area must be written using square units.
- Incorrect rearranging: Rearrange the complete formula carefully.
- Arithmetic errors: Check your multiplication and division.
- Exam Tips
- Check the height: Make sure it is perpendicular to the base.
- Write the formula: Start with A = ½bh before substituting.
- Show your working: Keep each calculation step clear.
- Check the units: Use cm², m² or the appropriate square unit.
- Practise rearranging: Be prepared to find a missing base or height.
Skills Used in Area of Triangles
Area of Parallelograms
Area of Trapeziums
Compound Shapes
Surface Area
Similar Shapes
Scale Drawings
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Area of Triangles Tutorial
Step-by-step walkthroughs of Area of Triangles with clear methods and exam tips.
Frequently Asked Questions
The height is the perpendicular distance from the chosen base to the opposite vertex.
Only if it is perpendicular to the chosen base. The height must meet the base at a 90° angle.
Substitute the known area and base into A = ½bh, then rearrange the equation to find the height.
Substitute the known area and height into A = ½bh, then rearrange the equation to find the base.
