Math Homework. Do It Faster, Learn It Better.

Word Problems Involving Width, Length, and Area

The formula for the area of a rectangle is

A = w × h

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

The formula for the area of a triangle is

A = 1 2 b × h

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

You'll often encounter word problems where two of the values in one of these formulas are given, and you're required to find the third.

Example 1:

A rectangular city block is divided into 56 square plots of equal size. If there are 14 plots along the length of the block, how many plots are there along the width of the block?

This is an area problem where the "unit" is a square plot. The city block is a rectangle with area 56 , and the length is 14 . Substitute in the formula.

56 = w × 14

Divide both sides by 14 .

4 = w

So, the city block is 4 plots wide.

Example 2:

Carlos is surveying a plot of land in the shape of a right triangle. The area of the land is 45,000 square meters. If one leg of the triangular plot is 180 meters long, what is the other leg of the triangle?

This is an area problem involving the formula for a triangle. Since it's a right triangle, one leg can be considered as the base, and the other as the height. Substitute 45000 for A and 180 for b in the formula.

45000 = 1 2 ( 180 ) h


45000 = 90 h

Divide both sides by 90 .

45000 90 = h

500 = h

The other leg of the triangle is 500 meters long.