Sheet № 223 · Foundation + Higher · AQA · Edexcel · OCR
Surface Area of a Triangular Prism –
Surface area of a triangular prism is a frequently tested GCSE Maths topic at both Foundation and Higher tiers. A triangular prism has five faces — two identical triangular ends and three rectangular faces. You need to calculate the area of each face and add them together. This guide explains the method clearly, works through examples at
§Key definitions
Question:
A triangular prism has a cross-section that is a right-angled triangle with base 6 cm and height 8 cm. The hypotenuse is 10 cm and the prism length is 15 cm. Find the total surface area.
Answer:
The total surface area is 408 cm².
Q1 (Foundation):
A triangular prism has a right-angled triangle cross-section with legs 3 cm and 4 cm. The prism is 10 cm long. Find the total surface area.
Q2 (Foundation):
A triangular prism has an isosceles triangle cross-section with base 10 cm, equal sides 13 cm, and height 12 cm. The prism is 20 cm long. Find the total surface area.
Q3 (Higher):
The total surface area of a triangular prism is 336 cm². The cross-section is a right-angled triangle with legs 5 cm and 12 cm. Find the length of the prism.
§Formulas to memorise
Area of a triangle = ½ × base × height
Area of a rectangle = length × width
Total SA = 2 × (area of triangle) + (sum of areas of 3 rectangles)
Worked example
A triangular prism has a cross-section that is a right-angled triangle with base 6 cm and height 8 cm. The hypotenuse is 10 cm and the prism length is 15 cm. Find the total surface area.
Working:
⚠ Common mistakes
- ✗Forgetting one of the rectangular faces. A triangular prism has three rectangular faces, not two. Make sure you include all three sides of the triangle as widths.
- ✗Using the slant height of the triangle instead of the perpendicular height. The area formula ½ × base × height requires the perpendicular height of the triangle, not the length of a slant side.
- ✗Confusing the prism length with the triangle base. The prism length (depth) is the dimension running between the two triangular faces. The triangle base is part of the cross-section.
✦ Exam tips
- →Sketch the net of the prism — it shows all five faces clearly, making it easier to calculate each area.
- →If the cross-section is a right-angled triangle, use Pythagoras' theorem to find the hypotenuse (the third side) if it is not given.
- →For isosceles or equilateral triangles, you may need to calculate the perpendicular height using Pythagoras.
- →Label each face with its dimensions before calculating — this avoids mixing up measurements.