Quadrilaterals are just the four-sided shapes (“quad” meaning four); they include:

Rectangles: four sides connected by four 90-degree angles

Rectangle Area Formula:

Squares: four sides of equal length connected by four 90-degree angles.

Square Area Formula:

Parallelograms: four-sided figure where opposite sides are parallel

Parallelogram Area Formula:

Parallelograms also have the nice property that opposite angles are of the same degree, and opposite sides are the same length.

Rhombus: a parallelogram with equal sides

Rhombus Area Formula:

Trapezoids: four-sided figure with one pair of parallel opposing sides

Trapezoid Area Formula:

Now a lot of these definitions overlap with others, so here is a diagram that explains how all of these shapes relate to one another:

Finally, one fact that is sometimes helpful in solving problems with quadrilaterals is:

Quadrilaterals Have 360 Degrees: The sum of the angles in a quadrilateral is 360.

This fact will come up again when we talk about finding the values of unknown angles.

Practice Problems:

1. Find the area of the entire figure below.

2. Find the area of the entire figure below.

3. The area of the below parallelogram is 30, is perpendicular to , and the ratio of the area of to the area of is 1 to 3. What is the value of ?

4. The dotted lines below meet at a right angle. Find