GMAT Math Quadrilateral and Solid Overview

GMAT CAT Quadrilateral

A quadrilateral is a four-sided polygon, and a polygon is any closed figure made of line segments that intersect. GMAT CAT primary ask you to find quadrilaterals' areas and perimeters. The measure of their perimeters is always the sum of their sides. Five main quadrilateral types are: squares, rectangles, parallelograms, rhombuses, and trapezoids.

Square : A square is a rectangle with four equal sides. It has four right angles, and its sides all have the same length. You can easily find its area if you know the length of only one side. The area of a square can be expressed as A = s² or A = s X s, where s is the length of a side.
Rectangle: A rectangle is a parallelogram with four right angles. Because rectangles are parallelograms, rectangles have all the properties of parallelograms. Use A = bh to find the area of a rectangle.
Rhombuses: A rhombus is a type of parallelogram. All four sides of a rhombus are equal in length, like a square, but a rhombus doesn't necessarily have four right angles. You can find the area of a rhombus by multiplying the lengths of the two diagonals and then dividing by 2.
Parallelograms: Most of the GMAT quadrilaterals are parallelograms. Parallelograms have properties that are very useful for solving GMAT problems:

• The opposite sides are parallel and equal in length.
• The opposite angles are equal in measure to each other.
• The measures of the adjacent angles add up to 180°, so they're supplementary to each other.
• The diagonals of a parallelogram bisect each other. In other words, they cross at the midpoint of both diagonals.

Trapezoids: A trapezoid is a quadrilateral with two parallel sides and two nonparallel sides. The parallel sides are called the bases, and the other two sides are called the legs.

GMAT CAT Solids

Solid geometry, or three-dimensional geometry, puts some depth to plane geometrical figures. Three-dimensional geometry is about as simple as plane geometry, and you can apply many of the same strategies. You'll most likely be asked no more than a handful of solid geometry questions on the GMAT, and they'll likely concern only rectangular solids and cylinders.

Rectangular Solids: You make a rectangular solid by taking a simple rectangle and adding depth. Good examples of rectangular solids are bricks, cigar boxes, etc. A rectangular solid has three dimensions: length, height, and width. You really only need to worry about two basic measurements of rectangular solids in the GMAT CAT: total surface area and volume.
Cylinders: A cylinder is a circle that grows straight up into the third dimension to become the shape of a can of soda. The bases of a cylinder are two congruent circles on different planes. The cylinders you see on the GMAT are right circular cylinders, which mean that the line segments that connect the two bases are perpendicular to the bases.

GMAT Geometry Topics

Below are the topics covered under GMAT Geometry. Click on them to learn more:

• GMAT Angle & Triangle
• GMAT Quadrilateral & Solid
• GMAT Circle & Coordinate

Related Topics

GMAT Math Arithmetic | GMAT Math Algebra | GMAT Math Geometry | GMAT Math Data Sufficiency | GMAT Math Problem Solving