Word Problems Involving Width, Length and Area

When you see a word problem, you know that you are going to have to extract the facts of the problem from the text. In order to make sure you understand the problem, you have to first be certain you understand all the words that are used, especially those involving math. If you can put into your own words what the problem is asking you to find, you are a good way towards being able to solve the word problem.

Once you've figured out what the word problem is asking, you must devise a plan to find the solution. You might want to look for a pattern, draw a diagram, set up variables to solve an equation, or something else. Follow through with the plan and then check to make sure your solution makes sense.

Width, length, and area

To find the area of a rectangle, we use the formula:

$A=wh$

where A is the area, w is the width, and h is the height of the rectangle.

To find the area of a triangle, we use the formula:

$A=\frac{1}{2}\left(b\right)\left(h\right)$

where A is the area, b is the base of the triangle, and h is the height.

Word problems involving width, length, and area will frequently give you two of these measurements and require you to solve for the third measurement.

Word problems with rectangles

A city block, in the shape of a rectangle, is divided into 56 square plots of equal size. There are 14 plots along the length of the block. How many plots are there along the width of the block?

This problem involves area, and the unit used is one square plot. The area of the city block is 56, and the length of the block is 14. Substitute in the formula:

$56=w\times 14$

To solve this problem, you use the inverse operation of multiplication, which is division. Divide both sides by 14 to isolate the width.

$\frac{56}{14}=w\times \frac{14}{14}$

$\frac{56}{14}=w$

$w\times 1=4$

Therefore, $w=4$ .

The width of the city block is 4 plots.

To check your answer, multiply 14 by 4, and you get 56. So your answer is correct.

Word problems with triangles

Maria is surveying a plot of land that is shaped like a right triangle. The area of the land is 45,000 square meters. If the bottom leg of the plot is 180 meters long, how long is the side leg of the triangular plot?

This is another area problem, this time using the formula to solve for the area of a triangle. Because it's a right triangle, one leg is considered the base and the other leg is considered the height. So we will substitute 45,000 for A (area) in the formula and 180 for b (base) in the formula.

$45000=\frac{1}{2}\times 180\times h$

First, we simplify the problem by multiplying $\frac{1}{2}$ by 180.

$45000=90h$

Then we isolate the h by dividing both sides by 90.

$\frac{45000}{90}=h$

$500=h$

This lets us know that the second leg of the triangular plot is 500 meters long.

We can check our answer by multiplying $180\times 500$ , which is 90,000, and multiplying that by $\frac{1}{2}$ , which is 45,000. Our answer is correct.

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Get help learning about word problems involving width, length, and area

Word problems of any kind can be especially challenging for some students. If your student needs help with word problems, specifically those involving width, length, and area, have them meet with a math tutor who can walk them through the steps and explain what's going on in a way that your student will understand. By going at your student's pace and using what they know about your student's learning style, a tutor can make their lessons as efficient and effective as possible. Contact Varsity Tutors and speak to one of our Educational Consultants today if you'd like to learn more about how tutoring can help your student understand word problems involving width, length, and area.