Area of 2D shapes: rectangle, triangle, trapezium and more
Calculate the perimeter and area of rectangles, triangles, parallelograms, trapeziums (trapezoids) and compound shapes, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolCurriculum fit: GCSE Maths Geometry and measures (Foundation and Higher). US: Grade 6-7 area and Geometry (Geometric Measurement and Dimension).
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What is it?
Perimeter is the total distance around the outside of a shape. Area is the amount of surface the shape covers, measured in square units such as cm².
For many shapes, area comes from a simple formula. For compound shapes, you split the shape into rectangles and triangles, or subtract one shape from another.
Key formulas and ideas
- Rectangle: area = length × width. Perimeter = 2(l + w).
- Triangle: area = ½ × base × perpendicular height.
- Parallelogram: area = base × perpendicular height.
- Trapezium: area = ½ × (a + b) × h, where a and b are the parallel sides.
Worked examples
Example 1: Triangle
Question: Find the area of a triangle with base 10 cm and perpendicular height 7 cm.
- Area = ½ × base × height.
- = ½ × 10 × 7 = 35.
Answer: 35 cm²
Example 2: Trapezium
Question: A trapezium has parallel sides 6 cm and 10 cm and height 4 cm. Find its area.
- Area = ½ × (6 + 10) × 4.
- = ½ × 16 × 4 = 32.
Answer: 32 cm²
Example 3: Compound shape
Question: An L-shape is made from a 8 cm by 3 cm rectangle with a 2 cm by 4 cm rectangle attached. Find its area.
- First rectangle: 8 × 3 = 24.
- Second rectangle: 2 × 4 = 8.
- Total: 24 + 8 = 32.
Answer: 32 cm²
Common mistakes
- Using the slant height instead of the perpendicular height.
- Forgetting the ½ for a triangle.
- Mixing up perimeter (length) and area (square units).
- Using different units in the same calculation.
Practice questions
Frequently asked questions
Why is area measured in square units?
Because it counts how many unit squares fit inside the shape.
How do I find the area of a shape with a hole?
Find the area of the whole shape and subtract the area of the hole.
Related guides
Area and circumference of a circle: formulas and examples
Learn the area and circumference formulas for circles, how to use radius and diameter, and how to work with semicircles, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolVolume and surface area of 3D shapes: formulas and examples
Find the volume and surface area of cuboids, prisms, cylinders, cones and spheres, with worked examples and a quick formula list.
GCSEHigh SchoolPythagoras' theorem: how to find a missing side
Use a² + b² = c² to find any side of a right-angled triangle. Worked examples for GCSE, and the Pythagorean theorem in US Geometry.
KS3GCSEMiddle SchoolHigh SchoolSources and review
- DfE: GCSE mathematics subject content and assessment objectives
- Common Core State Standards: Mathematics (high school)
Reviewed by StudyMorrow editorial review on 5 Nov 2026.