Area & Perimeter Reference Cheat Sheet

A printable reference covering area, perimeter, rectangles, triangles, parallelograms, trapezoids, circles, and composite figures for grades 3-7.

TopicsArea and Perimeter Measurement Shapes Geometry

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Math Vocabulary

Area and perimeter are measurements used to describe flat shapes. Perimeter tells how far it is around a shape, while area tells how much space is inside it. This cheat sheet helps students choose the right formula, label measurements correctly, and avoid mixing up units. It is useful for classwork, homework, test review, and real-world measurement problems. The most important idea is to match each shape with its formula before substituting numbers. Rectangles use length and width, triangles use base and height, and circles use radius or diameter. Composite figures can be split into simpler shapes, then the areas or perimeters can be combined. Always use linear units for perimeter, such as $\text{cm}$ , and square units for area, such as $\text{cm}^2$ .

Key Facts

The perimeter of a rectangle is $P = 2l + 2w$ , where $l$ is length and $w$ is width.
The area of a rectangle is $A = lw$ , so multiply length by width.
The area of a triangle is $A = \frac{1}{2}bh$ , where $b$ is the base and $h$ is the perpendicular height.
The area of a parallelogram is $A = bh$ , because it can be rearranged into a rectangle.
The area of a trapezoid is $A = \frac{1}{2}(b_1 + b_2)h$ , where $b_1$ and $b_2$ are the parallel bases.
The circumference of a circle is $C = 2\pi r$ or $C = \pi d$ , where $r$ is radius and $d$ is diameter.
The area of a circle is $A = \pi r^2$ , so the radius must be squared before multiplying by $\pi$ .
For composite figures, find the area or perimeter of smaller parts, then add or subtract as needed.

Vocabulary

Area: Area is the amount of flat space inside a shape, measured in square units such as $\text{cm}^2$ .
Perimeter: Perimeter is the total distance around a polygon, found by adding all side lengths.
Circumference: Circumference is the distance around a circle, found with $C = 2\pi r$ or $C = \pi d$ .
Base: A base is the side of a shape used with its height in an area formula.
Height: Height is the perpendicular distance from a base to the opposite side or vertex.
Composite Figure: A composite figure is a shape made from two or more simpler shapes.

Common Mistakes to Avoid

Using perimeter when the problem asks for area is wrong because perimeter measures the outside boundary, not the space inside.
Forgetting square units for area is wrong because area counts unit squares, so a rectangle measured in $\text{cm}$ has area in $\text{cm}^2$ .
Using a slanted side as the height of a triangle or parallelogram is wrong unless it is perpendicular to the base.
Forgetting the factor $\frac{1}{2}$ in triangle or trapezoid formulas is wrong because those shapes use half of a related rectangle or parallelogram area.
Squaring the diameter in $A = \pi r^2$ is wrong because the formula uses the radius, and $r = \frac{d}{2}$ .

Practice Questions

1 Find the perimeter and area of a rectangle with length $12\text{ m}$ and width $5\text{ m}$ .
2 Find the area of a triangle with base $10\text{ cm}$ and height $7\text{ cm}$ .
3 Find the circumference and area of a circle with radius $4\text{ in}$ , using $\pi \approx 3.14$ .
4 A student says two shapes with the same perimeter must have the same area. Explain why this is not always true.

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