Sheet № 165 · Foundation + Higher · AQA · Edexcel · OCR
Area of a Triangle –
The area of a triangle is one of the most fundamental skills in GCSE Maths. At Foundation level you need the classic half-base-times-height formula, while Higher tier students must also learn A = ½ab sin C for triangles where the perpendicular height is not given.
§Key definitions
Question:
A triangle has a base of 10 cm and a perpendicular height of 6 cm. Find its area.
Q1 (Foundation):
A triangle has a base of 14 cm and a perpendicular height of 9 cm. Find its area.
Q2 (Foundation):
The area of a triangle is 36 cm². The perpendicular height is 8 cm. Find the base.
Q3 (Higher):
Triangle ABC has AB = 11 cm, AC = 7 cm, and angle A = 54°. Find the area to 1 decimal place.
§Formulas to memorise
A = ½ × base × perpendicular height
A = ½ab sin C, where a and b are two sides and C is the included angle between them (Higher tier)
A = ½ × base × height
A = ½ × 10 × 6
A = ½ × 60
A = 30
A = ½ab sin C
A = ½ × 9 × 12 × sin 40°
A = 54 × 0.6428…
A = 34.7 (1 d.p.)
Worked example
A triangle has a base of 10 cm and a perpendicular height of 6 cm. Find its area.
Working: A = ½ × base × height A = ½ × 10 × 6 A = ½ × 60 A = 30
⚠ Common mistakes
- ✗Using the slant side instead of the perpendicular height. The height must be at right angles to the base, not along a side of the triangle. Look for the right-angle marker on the diagram.
- ✗Forgetting to halve. The ½ is essential — without it you calculate the area of a full rectangle, which is double the triangle.
- ✗Using the wrong angle in ½ab sin C. The angle must be the one enclosed between the two sides you are using, not any angle in the triangle.
- ✗Calculator in wrong mode. When using sin, ensure your calculator is set to degrees, not radians.
- ✗Not including square units. Area is always in cm², m², etc. — never cm or m.
✦ Exam tips
- →Always write the formula first — this secures a method mark even if your arithmetic slips.
- →If a triangle is part of a compound shape, calculate its area separately then add or subtract.
- →For ½ab sin C questions, clearly state the two sides and the included angle before substituting.