On GMAT Test Day, you will likely see at least a few quadrilaterals tested. Quadrilaterals, like other shapes in Geometry, usually appear in Geometry questions that involve basic properties of quadrilaterals, perimeter, or area. Like most Geometry, all it takes is some memorization and a little practice!
A quadrilateral, by definition, is a polygon with four sides created by four straight lines. Some common quadrilaterals are: a square, a rectangle, a parallelogram, and a trapezoid.
Need-to-know fact: The sum of the interior angles of any quadrilateral is 360.
Remember that every time you add a side to a figure, you add 180 degrees to the sum of its interior angles. That is why a triangle’s sum is 180, and any quadrilateral’s sum is 360. Keep in mind that definition-wise, quadrilaterals are inclusive. This means that a square is ALSO a rectangle, so be aware that just because a question states that a shape is a “rectangle” doesn’t necessarily mean it can’t have four equivalent sides!
The perimeter of a quadrilateral is the sum of its four sides. For a rectangle, the formula is P = l + l + w + w, or P = 2l + 2w. For a square, this becomes P = 4s. For other quadrilaterals, you need to know the length of each side in order to find the perimeter, unless you are given more information about the comparative lengths of the sides. For example, for a parallelogram we know that the opposite sides are equal in value, so knowing two adjacent sides would be sufficient to find the perimeter.
The area of a quadrilateral is the measurement contained within its four sides. There is no one area formula for all quadrilaterals. Instead, each one has a unique equation that must be memorized.
- To find the area of a square, we use the formula A = s2, where s = side of the square.
- To find the area of a rectangle, we use the formula A = lw, where l = length and w = width. T
- To find the area of a parallelogram, we use the formula A = bh, where b = base and h = height. We do NOT simply multiply the two side lengths. Remember the base and the height must be perpendicular.
- To find the area of a trapezoid, we use the formula A = h(b1 + b2) / 2. We essentially take the average of the two bases, and multiply it by the height. Again, the height is perpendicular to each base.
Remember to analyze your incorrect questions from Veritas Prep’s question bank. Use this data to understand your strengths and weaknesses and focus your GMAT prep on the area that need it most!
Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT.