Word Problems Involving Width, Length, and Area
The formula for the area of a rectangle is
where is the area, is the width, and is the height.
The formula for the area of a triangle is
where is the area, is the base and 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 square plots of equal size. If there are 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 , and the length is . Substitute in the formula.
Divide both sides by .
So, the city block is plots wide.
Example 2:
Carlos is surveying a plot of land in the shape of a right triangle. The area of the land is square meters. If one leg of the triangular plot is 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 for and for in the formula.
Simplify.
Divide both sides by .
The other leg of the triangle is meters long.