Calculate area and perimeter for rectangles, circles, triangles, trapeziums, parallelograms, and sectors
Calculating area and perimeter is a fundamental skill in geometry, tested throughout the UK maths curriculum from Key Stage 2 through to A-level. Area measures the amount of two-dimensional space inside a shape, while perimeter measures the total distance around the boundary of a shape. Our calculator handles six common 2D shapes: rectangles, circles, triangles, trapeziums, parallelograms, and sectors. Each calculation shows the relevant formula and provides step-by-step working, making it ideal for GCSE maths revision. The calculator uses UK spelling throughout, including "trapezium" rather than the American "trapezoid." Understanding area and perimeter is essential for real-world applications such as calculating flooring, paint coverage, fencing requirements, and land measurement. These practical applications appear frequently in GCSE context questions set by AQA, Edexcel, OCR, and WJEC exam boards. At GCSE Higher tier, students must know area formulas for all standard shapes, including the trapezium formula (which is provided on the formulae sheet) and the sector formula. They should also be able to apply Heron's formula when three sides of a triangle are known but the height is not. The National Curriculum requires students to calculate areas of compound shapes by dividing them into simpler shapes, calculate the area and circumference of circles using pi, and find the area of sectors and segments. Our calculator covers all of these individual shape calculations with clear formula explanations and working that matches the approach expected in exam answers.
To calculate area and perimeter: 1. Select the shape from the dropdown menu: rectangle, circle, triangle, trapezium, parallelogram, or sector. 2. Enter the relevant measurements for your chosen shape. Different shapes require different inputs. For a rectangle, enter length and width. For a circle, enter the radius. For a triangle, enter the base and height, or all three sides to use Heron's formula. 3. For a trapezium, enter both parallel sides and the perpendicular height between them. Optionally enter the non-parallel sides to calculate the perimeter. 4. For a sector, enter the radius and the central angle in degrees. The calculator finds both the sector area and the arc length. 5. Review the results showing area and perimeter (or circumference for circles, arc length for sectors), along with the formula used and step-by-step working. 6. Use the working to check your own calculations or as a model for exam-style answers. Remember that GCSE examiners award marks for showing the formula, substitution, and the final answer with correct units.
Area and perimeter formulas for common shapes: Rectangle: Area = length * width. Perimeter = 2 * (length + width). Example: length = 5, width = 3. Area = 15 cm^2. Perimeter = 16 cm. Circle: Area = pi * r^2. Circumference = 2 * pi * r. Example: radius = 7. Area = pi * 49 = 153.94 cm^2. Circumference = 2 * pi * 7 = 43.98 cm. Triangle: Area = 0.5 * base * height. Perimeter = sum of all three sides. Heron's formula (when all three sides are known): s = (a + b + c) / 2, then Area = sqrt(s(s-a)(s-b)(s-c)). Trapezium: Area = 0.5 * (a + b) * h, where a and b are the parallel sides and h is the perpendicular height. Example: parallel sides 3 and 5, height 4. Area = 0.5 * (3 + 5) * 4 = 16 cm^2. Parallelogram: Area = base * perpendicular height. Perimeter = 2 * (base + side). Sector: Area = (angle / 360) * pi * r^2. Arc length = (angle / 360) * 2 * pi * r. Example: radius 10, angle 90 degrees. Area = (90/360) * pi * 100 = 78.54 cm^2. Arc = (90/360) * 2 * pi * 10 = 15.71 cm. All of these formulas are covered in the GCSE maths specification. The circle, sector, and trapezium formulas are provided on the exam formulae sheet, but students should be familiar with all of them.