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This lesson is part of a series of lessons for the quantitative reasoning section of the GRE revised General Test. In this lesson, we will learn:

- quadrilaterals; squares, rectangles, parallelograms, trapezoids
- area of quadrilaterals

Every quadrilateral has four sides and four interior angles. The measures of the interior angles add up to 360°.

The following are special quadrilaterals.

• A quadrilateral with four right angles is called a rectangle. Opposite sides of a rectangle are parallel and congruent, and the two diagonals are also congruent.

PQ = SR, PS = QR and PR = QS

• A rectangle with four congruent sides is called a square.

• A quadrilateral in which both pairs of opposite sides are parallel is called a parallelogram. In a
parallelogram, opposite sides are congruent and opposite angles are congruent. Rectangles and squares are also parallelograms.

PQ = SR and PS = QR

• A quadrilateral in which two opposite sides are parallel is called a trapezoid.

*l * is parallel to *m *

The following video shows how to classifying quadrilaterals based on the given information.

For all parallelograms, including rectangles and squares, the area *A* equals the product of the length of a
base *b* and the corresponding height *h*; that is,

A = bh

Any side can be used as a base. The height corresponding to the base is the perpendicular line segment from any point of a base to the opposite side (or an extension of that side).

Below are examples of finding the areas of a square, a rectangle and a parallelogram.

The area *A* of a trapezoid equals half the product of the sum of the lengths of the two parallel sides
*a *and* b *and and the corresponding height *h*; that is,

Area of trapezoid

This video gives formulas and examples for how to find the area of squares, rectangles, triangles, parallelograms, and trapezoids. The video also explains the difference between base and height.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.