Area and Perimeter of Basic Figures
Overview
Every flat figure has two basic measurements. The perimeter is the distance around the outside of the figure, and the area is the amount of surface the figure covers. This lesson reviews the area formulas for the basic figures — parallelograms, triangles, trapezoids, and circles — and uses the Pythagorean Theorem to find a missing side when a figure does not give you every length you need.
Vocabulary
- Area
- The number of square units contained within a figure. Area is always measured in units squared (units²).
- Perimeter
- The number of linear units around the outside of a figure — the sum of the lengths of its sides.
- Circumference
- The distance around the outside of a circle: C = 2πr.
- Base and Height
- For area formulas, the height is the perpendicular distance to the base — not a slanted side length.
Main Ideas
- Parallelogram: A = bh. Triangle: A = ½bh. Trapezoid: A = ½(b₁ + b₂)h. Circle: A = πr².
- Perimeter is simply the sum of the sides that make up the outside of the figure.
- If a side length is missing, find it first — often with the Pythagorean Theorem — before computing area or perimeter.
- For an isosceles trapezoid, the smaller base is centered over the longer base, so the overhang on each side is half the difference of the bases.
- Area of a rhombus can also be found from its diagonals: A = ½d₁d₂.
- Keep the units straight: perimeter in units, area in units².
Lesson Notes
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Practice Problems
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Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.