How to Calculate Area and Perimeter
Learn how to calculate the area and perimeter of common shapes including squares, rectangles, triangles, and circles. Step-by-step formulas with worked examples for each shape.
Understanding Area vs. Perimeter
Area measures the amount of two-dimensional space enclosed by a shape, expressed in square units such as cm² or ft². Perimeter measures the total length of a shape's boundary, expressed in linear units. Knowing both is essential for tasks like fencing a yard (perimeter) or tiling a floor (area).
Rectangles and Squares
For a rectangle with length l and width w, the area is A = l × w and the perimeter is P = 2(l + w). A square is a special rectangle where all sides are equal, so A = s² and P = 4s. For example, a rectangle measuring 8 m by 5 m has an area of 40 m² and a perimeter of 26 m.
Triangles
The area of a triangle is A = ½ × base × height, where the height is perpendicular to the base. The perimeter is simply the sum of all three sides: P = a + b + c. For a right triangle with legs 3 and 4, the area is ½ × 3 × 4 = 6 square units.
Circles
For a circle with radius r, the area is A = πr² and the circumference (perimeter) is C = 2πr. Using π ≈ 3.14159, a circle with radius 5 cm has an area of approximately 78.54 cm² and a circumference of approximately 31.42 cm. Remember to use the radius, not the diameter, in these formulas.
Parallelograms and Trapezoids
A parallelogram has area A = base × height, where height is perpendicular to the base. A trapezoid with parallel sides a and b and height h has area A = ½(a + b)h. For a trapezoid with parallel sides 6 and 10 and height 4, the area is ½(6 + 10) × 4 = 32 square units.
Irregular Shapes
For irregular shapes, one common approach is to divide the shape into simpler components, calculate each area separately, and add them together. Another method is the coordinate geometry approach, where you use the Shoelace formula: A = ½|Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)| for a polygon defined by vertices.
Try These Calculators
Put what you learned into practice with these free calculators.
Related Guides
How to Calculate Volume of 3D Shapes
Learn how to calculate the volume of common 3D shapes including cubes, rectangular prisms, cylinders, cones, and spheres. Step-by-step formulas with real examples.
How to Use the Pythagorean Theorem
Learn how to apply the Pythagorean theorem to find the sides of a right triangle. Covers the formula, common Pythagorean triples, and real-world applications in construction, navigation, and geometry.
How to Calculate Ratios and Proportions
Learn how to set up and solve ratios and proportions with clear examples. Understand the difference between ratios and proportions and apply them in real-world situations like recipes, maps, and scaling.