Sheetworks
Create

Generate Perimeter, Area & Volume Worksheets

Calculate perimeter, area, and volume using formulas with given dimensions. Apply formulas for rectangles, triangles, circles, and 3D shapes.

Measuring Shapes: Perimeter, Area & Volume

Perimeter measures the distance around a flat shape, area measures the surface it covers, and volume measures the space a three-dimensional object occupies. These formulas are used constantly in construction, landscaping, packaging, cooking, and any situation that involves measuring or fitting objects into spaces.

Components of Perimeter, Area & Volume

This section covers the essential formulas:

  • Perimeter: The sum of all side lengths of a polygon. For a rectangle: P = 2l + 2w. For a regular polygon: P = n × s.
  • Area of 2D Shapes: Rectangle: A = l × w. Triangle: A = 1/2 × b × h. Parallelogram: A = b × h. Trapezoid: A = 1/2 × (b₁ + b₂) × h.
  • Surface Area: The total area covering the outside of a 3D object. Rectangular prism: SA = 2lw + 2lh + 2wh.
  • Volume: The space inside a 3D object. Rectangular prism: V = l × w × h. Cylinder: V = π × r² × h. Triangular prism: V = 1/2 × b × h × l.

Examples of Perimeter, Area & Volume

Perimeter Examples

  • A rectangle is 12 cm long and 7 cm wide. P = 2(12) + 2(7) = 24 + 14 = 38 cm.
  • A regular hexagon has sides of 5 m. P = 6 × 5 = 30 m.
  • A garden bed has sides of 8 ft, 10 ft, 8 ft, and 10 ft. P = 8 + 10 + 8 + 10 = 36 ft of fencing needed.

Area Examples

  • A rectangular room is 15 ft by 12 ft. A = 15 × 12 = 180 square feet of flooring.
  • A triangle has base 10 cm and height 6 cm. A = 1/2 × 10 × 6 = 30 cm².
  • A trapezoid has parallel sides of 8 m and 14 m with a height of 5 m. A = 1/2 × (8 + 14) × 5 = 1/2 × 22 × 5 = 55 m².

Surface Area Examples

  • A box is 4 cm × 3 cm × 2 cm. SA = 2(4 × 3) + 2(4 × 2) + 2(3 × 2) = 24 + 16 + 12 = 52 cm².
  • A cube with 5-inch sides has SA = 6 × 5² = 6 × 25 = 150 square inches.
  • Wrapping a gift box that is 30 cm × 20 cm × 10 cm requires at least 2(600) + 2(300) + 2(200) = 2,200 cm² of paper.

Volume Examples

  • A rectangular box is 8 cm × 5 cm × 3 cm. V = 8 × 5 × 3 = 120 cm³.
  • A cylinder has radius 4 inches and height 10 inches. V = π × 4² × 10 = 160π ≈ 502.7 cubic inches.
  • A swimming pool is 25 m long, 10 m wide, and 2 m deep. V = 25 × 10 × 2 = 500 m³ of water.