Quadrilaterals Reference Cheat Sheet

A printable reference covering quadrilateral types, angle sums, perimeter, area of rectangles, squares, parallelograms, trapezoids, and rhombuses for grades 6-8.

Download PNG

Related Tools

Related Labs

Related Worksheets

Related Infographics

This quadrilaterals reference covers the main properties, angle rules, perimeter formulas, and area formulas students need in middle school geometry. It helps students compare rectangles, squares, parallelograms, rhombuses, trapezoids, and kites without mixing up their features. A clear reference sheet is useful because many quadrilaterals share properties but do not share all formulas or angle relationships. The most important idea is that every quadrilateral has four sides and interior angles that add to $360^\circ$ . Perimeter is found by adding all side lengths, while area depends on the shape and the correct height. Parallel sides, equal sides, right angles, and diagonals help identify each quadrilateral. Students should always match the formula to the shape and use perpendicular height when finding area.

Key Facts

The interior angle sum of every quadrilateral is $360^\circ$ .
The perimeter of any quadrilateral is $P = a + b + c + d$ .
The area of a rectangle is $A = lw$ , where $l$ is length and $w$ is width.
The area of a square is $A = s^2$ , and its perimeter is $P = 4s$ .
The area of a parallelogram is $A = bh$ , where $h$ is the perpendicular height, not the slanted side.
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 area of a rhombus or kite using diagonals is $A = \frac{1}{2}d_1d_2$ .
Opposite angles in a parallelogram are equal, and consecutive angles in a parallelogram add to $180^\circ$ .

Vocabulary

Quadrilateral: A polygon with exactly $4$ sides and $4$ angles.
Parallelogram: A quadrilateral with two pairs of parallel opposite sides.
Trapezoid: A quadrilateral with at least one pair of parallel sides.
Rhombus: A parallelogram with $4$ equal side lengths.
Diagonal: A segment that connects two nonadjacent vertices of a polygon.
Height: The perpendicular distance from a base to the opposite side or vertex.

Common Mistakes to Avoid

Using the slanted side as the height is wrong because area formulas such as $A = bh$ require the perpendicular height.
Forgetting to add all four sides for perimeter is wrong because perimeter measures the total distance around the shape, so $P = a + b + c + d$ .
Using $A = lw$ for every quadrilateral is wrong because rectangles use $A = lw$ , but parallelograms use $A = bh$ and trapezoids use $A = \frac{1}{2}(b_1 + b_2)h$ .
Assuming every parallelogram is a rectangle is wrong because a parallelogram does not need to have $90^\circ$ angles.
Adding only one base in the trapezoid area formula is wrong because the formula uses the sum of both parallel bases, $A = \frac{1}{2}(b_1 + b_2)h$ .

Practice Questions

1 A rectangle has length $12\text{ cm}$ and width $5\text{ cm}$ . Find its area and perimeter.
2 A parallelogram has base $9\text{ in}$ and perpendicular height $4\text{ in}$ . Find its area.
3 A trapezoid has bases $6\text{ m}$ and $14\text{ m}$ with height $5\text{ m}$ . Find its area.
4 A shape has two pairs of parallel sides and all four sides are equal, but its angles are not $90^\circ$ . Which quadrilateral is it, and why?

Sign in to save