Quadrilateral Properties Chart Cheat Sheet

A printable reference covering quadrilateral properties, parallelograms, rectangles, rhombuses, squares, trapezoids, kites, angle sums, and area formulas for grades 5-9.

Download PNG

Related Tools

Related Labs

Related Worksheets

Related Infographics

This quadrilateral properties chart organizes the most important facts about four-sided figures in one printable reference. Students need it to compare shapes, identify special quadrilaterals, and choose the correct area formula. It is especially useful when problems ask whether a shape is a parallelogram, rectangle, rhombus, square, trapezoid, or kite. The chart helps connect side lengths, angles, diagonals, and symmetry in a clear way. Every quadrilateral has an interior angle sum of $360^\circ$ , but special quadrilaterals have extra rules. Parallelograms have opposite sides parallel and congruent, while rectangles, rhombuses, and squares add special angle or side conditions. Trapezoids have one pair of parallel sides, and kites have two pairs of adjacent congruent sides. Area formulas such as $A = bh$ , $A = \frac{1}{2}h(b_1 + b_2)$ , and $A = \frac{1}{2}d_1d_2$ are the core tools for solving measurement problems.

Key Facts

The interior angles of every quadrilateral add to $360^\circ$ .
A parallelogram has both pairs of opposite sides parallel, opposite sides congruent, opposite angles congruent, and diagonals that bisect each other.
The area of a parallelogram is $A = bh$ , where $b$ is the base and $h$ is the perpendicular height.
A rectangle is a parallelogram with four right angles, so each angle measures $90^\circ$ and its area is $A = lw$ .
A rhombus is a parallelogram with four congruent sides, perpendicular diagonals, and area $A = \frac{1}{2}d_1d_2$ .
A square is both a rectangle and a rhombus, so it has four congruent sides, four right angles, and area $A = s^2$ .
A trapezoid has one pair of parallel bases, and its area is $A = \frac{1}{2}h(b_1 + b_2)$ .
A kite has two pairs of adjacent congruent sides, one pair of opposite congruent angles, perpendicular diagonals, and area $A = \frac{1}{2}d_1d_2$ .

Vocabulary

Quadrilateral: A quadrilateral is a polygon with exactly $4$ sides and an interior angle sum of $360^\circ$ .
Parallelogram: A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel.
Rectangle: A rectangle is a parallelogram with four right angles, each measuring $90^\circ$ .
Rhombus: A rhombus is a parallelogram with four congruent sides.
Trapezoid: A trapezoid is a quadrilateral with one pair of parallel sides called bases.
Diagonal: A diagonal is a segment that connects two nonadjacent vertices of a polygon.

Common Mistakes to Avoid

Confusing rectangles and parallelograms is wrong because every rectangle is a parallelogram, but not every parallelogram has four $90^\circ$ angles.
Calling every rhombus a square is wrong because a rhombus only needs four congruent sides, while a square also needs four $90^\circ$ angles.
Using slanted side length as height is wrong because formulas like $A = bh$ require the perpendicular height, not the length of an angled side.
Forgetting to add both trapezoid bases is wrong because the trapezoid area formula is $A = \frac{1}{2}h(b_1 + b_2)$ , not $A = \frac{1}{2}hb_1$ .
Assuming all quadrilateral diagonals are equal is wrong because equal diagonals are guaranteed in rectangles and squares, but not in all parallelograms, rhombuses, trapezoids, or kites.

Practice Questions

1 A parallelogram has base $b = 12\text{ cm}$ and height $h = 7\text{ cm}$ . Find its area.
2 A trapezoid has bases $b_1 = 9\text{ m}$ and $b_2 = 15\text{ m}$ with height $h = 6\text{ m}$ . Find its area.
3 A rhombus has diagonals $d_1 = 10\text{ in}$ and $d_2 = 14\text{ in}$ . Find its area.
4 A quadrilateral has four congruent sides but no right angles. Which special quadrilateral is it, and why is it not a square?

Sign in to save