GMAT Quantitative Review

3.0 Math Review

3.3 Geometry

7. Quadrilaterals

A polygon with four sides is a quadrilateral. A quadrilateral in which both pairs of opposite sides are parallel is a parallelogram. The opposite sides of a parallelogram also have equal length.

image

In parallelogram JKLMimage and imageimage and image.

The diagonals of a parallelogram bisect each other (that is, image and image).

The area of a parallelogram is equal to

image.

The area of JKLM is equal to image.

A parallelogram with right angles is a rectangle, and a rectangle with all sides of equal length is a square.

image

The perimeter of image and the area of WXYZ is equal to image.

The diagonals of a rectangle are equal; therefore image.

image

A quadrilateral with two sides that are parallel, as shown above, is a trapezoid. The area of trapezoid PQRS may be calculated as follows:

image.