If there’s one thing you’re guaranteed to see on the GED Mathematical Reasoning test, it’s word problems. The GED math test cares more about your critical thinking and problem-solving skills than your ability to crunch numbers, so you are very likely to come across questions that wrap the math content into real-life scenarios that will require you to figure out exactly which calculations you’ll need to do to solve.

This is especially true in geometry, where you’ll be expected to apply geometric formulas to all sorts of situations. Luckily, the GED Testing Service has made it a lot easier for you by providing a formula sheet that you can use during the test, so you won’t have to have any of these formulas memorized. What you will have to do is know when and how to use them. For an overview of these formulas and how they work, start here.

Here is a guide to GED geometry word problems, including commonly-used scenarios, plenty of examples, and some practice questions for you to try on your own. Master these skills and you’ll be well on your way to GED math success.

## Perimeter

Perimeter is the distance around a shape. Some common setups for word problems involving perimeter include:

- Putting a fence around a yard
- Walking around a block or trail
- Putting up a border or trim

The basic way to find the perimeter of any polygon is to add up all of its side lengths; however, you will see the specific formulas for different types of shapes on your formula sheet.

#### Example: Rectangle

Bill has a rectangular garden that is 6 feet by 4 feet. He wants to put a fence around the garden. How much fencing does he need to buy?

##### Explanation

The formula for the perimeter of a rectangle is P= 2l+2w. The variable *l* is the length, and the variable *w* is the width.

**Tip:**Although the perimeter is the combined length of all sides, you only need to know two sides of a rectangle to find its perimeter.

We know the length and the width of the garden, so we can solve. Bill needs to buy 20 feet of fence:

P= 2l+2w

P= 2(6)+2(4)

P= 12+8

P= 20

**Tip:**A square is a special rectangle with four equal side lengths. You only need to know the length of one side to find the perimeter of a square: P= 4s

## Circumference

The perimeter of a circle has a special name: circumference. Circumference has two related formulas: C= 2πr or C= πd. The variable *r* is the radius. The variable *d* is the diameter. You can use 3.14 as the value of π.

#### Example

Chris is making a circular table cloth. He wants to trim the edge of the cloth with lace. The diameter of the table cloth is 70 inches. How much trim does Chris need?

##### Explanation

We know the diameter, so we can solve. Chris needs 219.8 inches of lace:

C= πd

C=(3.14)(70)

C=219.8

## Area

The area is the space contained inside a two-dimensional shape. We usually think of it as how many square units would fit inside of the shape. For this reason, the units of the area are labeled as square units (or units^{2}). Area word problems often involve:

- Buying fabric
- Covering a flat object, such as a floor or wall
- Making a floor plan

You find the area of a rectangle by multiplying its length by its width, and in general the formulas for finding the area of all other shapes (except circles) are derived from this basic concept.

#### Example: Square

Ann wants to cover the square bulletin board in her classroom with fabric. She measured the bottom edge of the bulletin board to be 4 feet long. How many square feet of fabric should Ann buy?

##### Explanation

**Tip:**Remember, the area of a rectangle is lw. Since a square has equal side lengths, you only need to know one side length to find the area: A= s x s= s^{2}.

Since the bulletin board is square, and we know the length of one side, we can find the area. Ann needs to buy 16 square feet of fabric:

A=s^{2}

A=4^{2}

A=16

## Surface Area

The surface area is the combined area of all the faces of a three-dimensional shape. For example, the surface area of a cube is the total area of all six of its sides. Like area, surface area is labeled as squared units. For word problems, some common surface area scenarios include:

- Wrapping a gift
- Using material to make a 3D-shape

Finding the surface area involves finding the area of each face, and adding all of those areas together. For most shapes, there is a specific formula, which you’ll find on your formula sheet.

#### Example: Right Prism

Fred wants to wrap a box of candy he’s giving his friend. The box is a triangular prism. The base of the box has an area of 4 square inches and a perimeter of 6 inches. The entire box, from end-to-end, is 4 inches long. Fred has 24 square inches of wrapping paper. Does he have enough to wrap the box?

##### Explanation

**Tip:**A right prism is a prism with sides that are perpendicular to its bases. This describes most prisms you will come across.

The formula for a right prism is SA=ph+2B. The variable *p* is the perimeter of the base, the variable *B* is the area of the base, and the variable *h* is the height of the prism.

We know a lot about Fred’s box of candy. We know the perimeter and area of the base, and we know the height of the box (the length end-to-end). With all this information, we can calculate the surface area.

SA=ph+2B

SA=(6)(4)+2(4)

SA=24+8

SA=32

Fred doesn’t have enough wrapping paper to wrap the box. He would need 32 square inches.

## Volume

Volume is the space inside of a three-dimensional shape. Since a 3D shape has three dimensions, the volume is labeled in cubic units (units^{3}). For word problems, look for these common situations:

- Filling a pool with water
- Comparing the water capacity of different containers
- Finding a missing dimension of a 3D shape

Finding the volume essentially involves multiplying the three dimensions of the shape together. Since all shapes aren’t as easy to work with as cubes, however, prisms, cylinders, pyramids, cones, and spheres all have their special formulas, which you’ll find on your formula sheet.

#### Example: Cone

Erline needs conical paper cups for a science experiment. Each cup needs to hold 6 cubic inches of liquid. She finds cups that are 3 inches in diameter. How deep do the cups need to be in order to hold at least 10 cubic inches of liquid?

##### Explanation

The formula for the volume of a cone is ^{1}⁄_{3}πr^{2}h. We know the volume. Since we know the diameter (3), we can calculate the radius by dividing it in half (3/2=1.5).

**Tip:**The radius of a circle is always half its diameter.

Since we have all of this information, we can plug it into the formula and solve for the height (or, in the case of these cups, depth).

V= ^{1}⁄_{3}πr^{2}h

6= ^{1}⁄_{3} π(1.5)^{2}h

6= ^{1}⁄_{3}(3.14)(2.25)h

6= 2.355h

2.5478= h

Erline’s cups need to be at least 2.5478 inches deep.

## Practice GED Geometry Word Problems

Try these practice GED geometry word problems. See if you can figure out which type of calculation is needed. Then select the correct formula and solve. Answers are below.

1. The Happy Fish Tank comes in two models. Model A is 36 x 18 x 19 feet. Model B is 48 x 12 x 18. Which model holds more water?

A) Model A

B) Model B

C) They both hold the same amount.

D) Not enough information is given.

2. Three paths (A, B, and C) form the border of a triangular park in the middle of the city. Path A is 1.75 miles long. Path B is 1 mile long. Path C is 1.5 miles long. If Don wants to run 5 miles a day, will he meet his goal by running around the border of the park?

A) Yes

B) No

C) Not enough information is given.

3. Alesia is making a model farm for school. She wants to make 4 paper silos for her model. Each silo will be a cylinder 5 inches tall and 2 inches in diameter. How many square inches of paper does she need to make her silos?

A) 37.68 square inches

B) 40 square inches

C) 150.72 square inches

D) 351.68 square inches

4. Jay is covering a yard with sod. The yard is shaped like a trapezoid. The two parallel sides of the yard are 20 and 30 feet long. The shortest distance between those two sides is 32 feet. If sod costs 35 cents per square foot, how much will it cost Jay to cover the yard?

A) $224

B) $280

C) $640

D) $800

### Answer Key

1. A

This is a problem about water capacity, the amount of space inside a rectangular prism. That’s volume. The formula for the volume of a rectangular prism is V=lwh. We need to find the volume of each tank, and then compare.

Model A: V=(36)(18)(19)= 12,312 cubic feet

Model B: V=(48)(12)(18)= 10,368 cubic feet

Model A holds more water.

2. B

We know this is a perimeter question because the it is asking about the length of the border of a shape (a triangular park). The perimeter of a triangle is the sum of all its sides.

P=1.75+1+1.5=4.25

Since 4.25 is less than 5, Don will not meet his goal.

3. C

Since this is a problem about using a material to make a 3D shape, we know it’s surface area. The formula for finding the surface area of a cylinder is SA=2πrh+2πr^{2}. We know the height and the diameter. Since we can find the radius by dividing the diameter in half, we have all the information we need to solve:

SA=2πrh+2πr^{2}

SA=2π(1)(5)+2π1^{2}

SA=2π(5)+2π

SA=2(3.14)(5)+2(3.14)

SA=31.4+6.28

SA=37.68

So, she needs 37.68 square inches of paper to make 1 silo. But, she’s making 4 silos, so we need to multiply the surface area by 4:

37.68(4)=150.72

4. B

Since Jay is covering a flat shape, this is a matter of area. The area of a trapezoid is A= ½h(b_{1}+b_{2}). The bases of a trapezoid are its two parallel sides. So we know both bases and the height of Jay’s trapezoid:

A= ½h(b_{1}+b_{2})

A= ½(32)(20+30)

A= ½(32)(50)

A= ½(1600)

A= 800

So, it will take 800 square feet of sod to cover the yard. But, we want to know the total price, at 35 cents per square foot. So we multiply by 0.35:

800(0.35)=280

It will cost Jay $280.