Geometric Word Problems

Concept: Geometry is the area of mathematics that deals with points, lines, angles, two-dimensional shapes, and three-dimensional figures and is used to solve many common everyday problems. Geometric word problems use stories and sentences that contain numbers and descriptions of objects and shapes. They ask you to find the answer to a question, using formulas for finding areas, volumes, perimeters and much more. You can usually solve geometric word problems by using the following 5 basic steps.

Steps for Solving Geometric Word Problems

Step 1 | Read the word problem carefully and completely. Determine what the word problem is asking you to find out.
Step 2 | Determine what information given in the word problem is needed to solve the problem, and what information is not needed to solve the problem.
Step 3 | Determine which math operation(s) and formula(s) to use in solving the word problem.
Step 4 | Set up the math operation(s) and formula(s), and solve the problem.
Step 5 | Re-read the word problem to make sure that the solution makes sense, and that you answered the question that was asked. Write the final answer.

Formulas for Finding Area
Square | A = s2 |
Rectangle | A = lw |
Triangle | A = 1/2bh |
Circle | A = r2 |
Parallelogram | A = bh |
l
h
Trapezoid | A = 1/2(b1 + b2)h |

Formulas for Finding Volume
Figure | Name | Formula | Term Meanings
l
h
w
| Rectangular solid | V = l w h | l = length w = width h = height
s
| Cube | V = s 3 | s = side
r
h
| Cylinder |  | r = radius h = height (or length)
| cone |  | r = radius h = height
e (or w ) e
e (or l ) e
| Square pyramid or Rectangular pyramid (Use w and l instead of e 2 for Rectangular pyramids) | or | h = height e = edge or h = height l = length w = width
r w l h
w w l h
| Prism |  | l = length w = width h = height
| Sphere |  | r = radius

Formulas for Finding Perimeters and Circumferences
To find the perimeter of a polygon, add the lengths of its sides
To find the circumference of a circle use the formula

Example What is the volume, in cubic feet, of a truck that has inside dimensions of 7 feet high, 4 feet wide, and 2.5 feet deep?

Step 1 | Read the word problem carefully and completely. Determine what the word problem is asking you to find out. | Find the storage volume of the truck.
Step 2 | Determine what information given in the word problem is needed to solve the problem, and what information is not needed to solve the problem. | There is no excess information.
Step 3 | Determine which math operation(s) and formula(s) to use in solving the word problem. | Use the formula for finding volume of a rectangular solid.
Step 4 | Set up the math operation(s) and formula(s), | V = lwh
| and solve the problem. | V = 2.5 x 4 x 7 V = 70 cu. ft.
Step 5 | Re-read the word problem to make sure that the solution makes sense, and that you answered the question that was asked. Write the final answer. | Find the storage volume of the truck. V = 7 cu. ft.