Geometry is a huge part of the GED Mathematical Reasoning subject test and most geometry questions will require you to use at least one formula. The good news is you don’t have to memorize a single one. On the GED math test, you will be given a formula sheet that contains every single formula you might have to use to solve these questions. Take a look.

That doesn’t mean you’re totally off the hook, though. You’re given the formulas, but you still have to know how to use them. You have to be able to read a word problem, figure out which formula is needed, and input the correct numbers to solve the problem. Here is an overview of how to use the major GED geometry formulas.

## Abbreviations in GED Geometry Formulas

On the formula sheet, you’ll notice that the formulas are written using abbreviations for the various dimensions of the shapes. You need to make sure you understand what these abbreviations stand for so that you plug the right numbers into the formulas.

Abbreviation | Definition |
---|---|

A | Area |

s | Side length |

l | Length |

w | Width |

b | Length of the base (can be any side of a triangle or parallelogram; each of the parallel sides of a trapezoid) |

h | Height (line drawn from the top of the shape to the base, perpendicular to the base) |

r | Radius of a circle (distance from the center to the edge) |

d | Diameter of a circle (the widest distance all the way across a circle, passing through the center) |

P | Perimeter |

C | Circumference |

SA | Surface Area |

V | Volume |

B | Area of the base shape of a three-dimensional figure |

p | Perimeter of a base with area B |

a, b, c | Lengths of the sides of a right triangle; c is the hypotenuse |

## Perimeter

** Perimeter** is the distance around the outer edge of a shape.

Let’s look at an example problem:

John wants to build a fence around an area of his yard that measures 20 feet by 22 feet. How many linear feet of fencing does he need?

a) 44 feet

b) 84 feet

c) 220 feet

d) 440 feet

The correct answer is B. To find the perimeter of a rectangle, add up the lengths of its sides. Since the opposite sides of a rectangle are congruent, there are 2 sides that are 20 feet long and 2 sides that are 22 feet long.

P = 2l + 2w

P= 2(20) + 2(22)

P= 40 + 44

P = 84

The perimeter of a circle has a special name— ** circumference**. You can find the circumference using the radius. Sometimes, you might also be given the circumference and asked to work backwards to find the radius. Either way, it’s the same formula:

**C = 2πr**.

Here’s an example problem:

The circumference of a circle is 36π cm. What is the length of its radius?

a) 6 centimeters

b) 12 centimeters

c) 18 centimeters

d) 24 centimeters

The correct answer is C. The formula for the circumference of a circle is C= 2πr. Since you know the circumference is 36π cm, you can use the formula to solve for r:

C=2πr

36π=2πr

18= r

## Area

** Area** is a measure of how much two-dimensional space something covers. The GED may ask you about the area of a square, rectangle, parallelogram, trapezoid, or circle.

Common area word problems ask about dimensions of a floor or wall. Here’s an example:

Jaime wants to tile his bathroom floor. The room measures 12 feet by 6 feet. How many square feet of tile must he buy?

a) 18 square feet

b) 36 square feet

c) 58 square feet

d) 72 square feet

The correct answer is D. To cover the inside of a two-dimensional shape, in this instance, a rectangular bathroom floor, you must consider area. The formula for area is A=lw. The bathroom floor has a length of 12 feet and a width of 6 feet. So, to find its area, you would calculate:

A=lw

A=12(6)

A=72

Now let’s try one with the area of a circle.

Which expression describes the area of a circle that has a radius of 4 centimeters?

a) 8π square centimeters

b) 16π square centimeters

c) 32π square centimeters

d) 44π square centimeters

The correct answer is B. The formula for the area of a circle is A=πr^{2}, where r stands for the radius of the circle. So, to find the area:

A=πr^{2}

A=π4^{2}

A=16π

## Volume

** Volume** is how much space a three-dimensional object takes up. You can also think of it as the capacity of a container.

Take a look at the following example:

The figure below shows a cylinder. Which expression describes its volume?

a) 24π in^{3}

b) 48π in^{3}

c) 24 in^{3}

d) 48 in^{3}

The correct answer is B. The formula for the volume of a cylinder is V= πr^{2}h, where r equals the radius of the cylinder’s base, and h equals the height of the cylinder. The drawing labels the height and the diameter. The radius of a circle is half its diameter. So, if the diameter is 4 inches, its radius is 2 inches. You can now use the formula to solve:

V= πr^{2}h

V= π2^{2}(12)

V= π4(12)

V= π(48)

## Surface Area

* Surface area* is the outside area of all of the surfaces of a three-dimensional figure. For shapes with flat sides, like cubes and rectangular prisms, you just add up the areas of all of the sides. For shapes with curved sides, like spheres and cylinders, it’s a little less obvious, but luckily, you’re given the formula so you only have to plug in the numbers.

Let’s try a surface area example problem:

Eleanor needs to wrap the box shown below. How many square feet of wrapping paper does she need to buy in order to wrap the box?

a) 15 square feet

b) 23 square feet

c) 30 square feet

d) 46 square feet

The correct answer is D. Eleanor will be covering each side of the box. A box is a three-dimensional shape with 6 faces. Specifically, it is a rectangular prism. The total area of all faces of a prism is its surface area. To find the surface area of a rectangular prism, calculate the area of each face, and then sum all of their areas. You can also use the formula SA=2lw+2lh+2wh. In the formula, the expression lw gives the area of one of the faces shown in the diagram. The expressions lh and wh give the areas of the other two faces shown in the diagram. Each is multiplied by 2, because there are three hidden faces of the box, each corresponding to one of these three faces. (Remember that opposite sides of a rectangular prism are congruent.) So, you can use the formula to solve:

SA=2lw+2lh+2wh

SA=2(5)(3)+2(5)(1)+2(3)(1)

SA=30+10+6

SA=46

## Pythagorean Theorem

There is one more geometry formula you’ll definitely want to understand— the ** Pythagorean Theorem**. This formula tells you the relationship between the lengths of the sides of a right triangle. It is very important to remember that this formula ONLY applies to RIGHT triangles— triangles that have a right (90°) angle.

The Pythagorean Theorem is **a ^{2}+b^{2}= c^{2}**.

c is the length of the hypotenuse. The hypotenuse is the longest side of a right triangle— the one that’s across from the right angle. a and b are the lengths of the other two sides. It doesn’t matter which letter you use for which.

Here’s an example:

The hypotenuse of a right triangle is 13 centimeters long. The base of the triangle is 5 centimeters long. What is the height of the triangle?

a) 6 cm

b) 8 cm

c) 12 cm

d) 18 cm

The correct answer is C. You can find a missing side length of a right triangle by using the Pythagorean Theorem: a^{2}+b^{2}= c^{2}. Since you know the length of the hypotenuse and one other side (the base), you can use the formula to solve:

a^{2}+b^{2}=c^{2}

a^{2}+5^{2}=13^{2}

a^{2}+25=169

a^{s}=144

a=12

## More Math Resources

Keep your momentum going and try some of these other great resources to help you prep for the GED Mathematical Reasoning subject test.

- Find out more about what’s on the GED math test.
- Learn all about converting units of measurement, which can help you on some geometry problems.
- Try an online practice test.