The GED Math test's Geometry portion tests your ability to solve problems involving shapes, area, perimeter, volume, and the coordinate plane. You will be provided with a formula sheet, so the focus is on applying the formulas correctly to real-world problems.

Core Geometry Topics

• Area and Perimeter: You should be able to calculate the area and perimeter of common shapes, including triangles, squares, rectangles, circles, and irregular shapes. Questions often involve finding the missing side of a shape or the area of a shaded region within a larger shape.

• Volume and Surface Area: You'll need to calculate the volume and surface area of three-dimensional shapes such as cylinders, cones, pyramids, and rectangular prisms. These problems are typically presented in a practical context, like figuring out how much water a pool can hold or how much paint is needed to cover a box.

• Pythagorean Theorem: This is a key concept for solving problems involving right triangles. You should know how to use the formula, $a^2+b^2=c^2$, to find the length of a missing side.

• Coordinate Geometry: This involves plotting points and analyzing shapes on a coordinate plane. You might be asked to find the distance between two points, the midpoint of a line segment, or the equation of a line.

• Angles and Parallel Lines: You should understand the properties of different types of angles (e.g., complementary, supplementary, vertical) and the relationships between angles formed when a transversal intersects parallel lines.

The GED test questions are often multi-step problems that require you to combine two or more geometric concepts to find a solution.

AREA AND PERIMETER

For the TABE test, you need to know the difference between area and perimeter and how to calculate them for common shapes.

What's the difference?

• Area is the amount of space inside a flat, 2D shape. Think of it as the number of square tiles needed to cover a floor. Area is always measured in square units (like ft2 or cm2).

• Perimeter is the total distance around the outside of a flat shape. Think of it as the length of a fence you'd need to go around a garden. Perimeter is measured in linear units (like feet or cm).

Key Formulas You Need to Know

The TABE test often focuses on squares, rectangles, and triangles. Make sure you memorize these formulas.

Rectangle

• Perimeter = 2⋅ length + 2⋅ width, or $P=2l+2w$.

• Area = length ⋅ width, or $A=l\cdot w$.

Square

• Perimeter = 4⋅ side, or $P=4s$. (Since all sides are the same length)

• Area = side ⋅ side, or $A=s^2$.

Triangle

• Perimeter = side1 + side2 + side3, or $P=a+b+c$.

• Area = 21​⋅ base ⋅ height, or $A=\frac{1}{2}bh$. The height is the perpendicular distance from the base to the opposite corner.

How to Solve a Problem

1. Read the question carefully: The most common mistake is to calculate area when the question asks for perimeter, or vice versa. Look for keywords like "border," "fence," or "distance around" for perimeter, and "cover," "space," or "tile" for area.

2. Identify the shape and its measurements: Look at the given diagram or the information in the problem to find the shape's length, width, or side lengths.

3. Choose the correct formula: Based on the shape and what the question is asking for, select the right formula from the list above.

4. Plug the numbers into the formula and solve: Replace the variables in the formula with the numbers from the problem and do the math.

Example Problem:

A rectangular garden is 10 feet long and 5 feet wide.

• Question 1: What is the perimeter of the garden?

  • Formula: $P=2l+2w$

  • Calculation: $P=2(10)+2(5)=20+10=30$ feet.

• Question 2: What is the area of the garden?

  • Formula: $A=l\cdot w$

  • Calculation: $A=10\cdot 5=50$ square feet (50ft2).

  •