Area and Perimeter Review
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Learning Objectives
- 1Compute the area and perimeter of rectangles and squares with US customary (in, ft, yd) and metric (cm, m) units
- 2Apply the triangle area formula A = (1/2) x b x h using base and perpendicular height in either system
- 3Compute the area of a parallelogram using A = b x h with customary or metric units
- 4Distinguish area (square units like sq in or cm^2) from perimeter (length units like ft or m)
Mini Lesson
Area is the amount of flat space INSIDE a shape, measured in square units (sq in, sq ft, sq yd, cm^2, m^2). Perimeter is the total distance AROUND the outside of the shape, measured in regular length units (in, ft, yd, cm, m). Area answers "how much carpet covers the floor?" while perimeter answers "how much fence wraps the yard?" — two very different questions, two very different formulas. The formulas are the same whether your measurements are in US customary or metric units; only the labels change.
Rectangles and Squares
- Rectangle area: A = L x W (length times width).
- Rectangle perimeter: P = 2L + 2W, or equivalently 2 x (L + W).
- A square is a rectangle with all four sides equal, so A = s x s = s^2 and P = 4s.
- Always include the unit. Area: 24 sq in, 24 sq ft, 24 cm^2, or 24 m^2. Perimeter: 20 in, 20 ft, 20 cm, or 20 m.
Parallel Worked Examples: Rectangle 6 x 4
- US customary — rectangle with L = 6 ft, W = 4 ft. Area: A = 6 x 4 = 24 sq ft. Perimeter: P = 12 + 8 = 20 ft.
- Metric — rectangle with L = 6 m, W = 4 m. Area: A = 6 x 4 = 24 m^2. Perimeter: P = 12 + 8 = 20 m.
- Same arithmetic; only the unit labels change.
- Notice the units differ within each example: square units for area, regular length units for perimeter.
Triangles
- Triangle area: A = (1/2) x b x h, where b is the base and h is the perpendicular height.
- Perpendicular height means a straight line from the base up to the opposite vertex, meeting the base at a right angle.
- Triangle perimeter: just add the three side lengths together.
- Example (customary): base 10 in, height 6 in gives A = (1/2) x 10 x 6 = 30 sq in.
- Example (metric): base 10 cm, height 6 cm gives A = (1/2) x 10 x 6 = 30 cm^2.
Parallelograms
- Parallelogram area: A = b x h. Same as a rectangle, but h is the perpendicular height (NOT the slanted side).
- Parallelogram perimeter: 2 x (side a + side b), where the two slanted sides equal the two horizontal sides in pairs.
- A common mistake is to multiply the base by the slanted side. Always use the perpendicular height for area.
- Examples: a parallelogram with base 8 ft, height 5 ft has A = 40 sq ft. Same shape with base 8 m, height 5 m has A = 40 m^2.
Tip: area uses SQUARE units — sq in, sq ft, sq yd, cm^2, m^2. Perimeter uses regular length units — in, ft, yd, cm, m. If the unit ends in "squared," it is an area answer.
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