How to Solve Rectangle Area Problems Part 1

The area of a rectangle including square are the simplest to calculate.  As we have discussed in the previous post, they can be calculated by multiplying their length and the width. That is if a rectangle has area A, length l and width w, then,

A = l \times w or simply A = lw.

In this post, we are going to solve various problem involving area of rectangles.

Problem 1

The length of a rectangle is 12 centimeters and its width is 5 centimeters. What is its area?

Solution

Using the representation above, l = 12 and w = 5. Calculating the area, we have

A = 12(5) = 60.

The area is 60 square centimeters. 

Problem 2

The area of a rectangular garden is 20 square meters. Its width is 2.5 meters. What is its length?

Solution

In this problem, the missing is the length and the given are the area and the width. So, A = 20 and w = 2.5. Using the formula, we have

A = lw.

Substituting the values of A and w, we have

20 = l(2.5).

Since we are looking for l, we divide both sides of equation by 2.5. That is

\frac{20}{2.5} = \frac{l(2.5)}{2.5}.

Simplifying, we have 8 = l.

Therefore, the length of the rectangular garden is equal to 8 meters.

Problem 3

The floor of a room 8 meters by 6 meters is to be covered with square tiles. The tiles dimensions is 25 centimeters by 25 centimeters. How many tiles are needed to covered the room? Note: 1 meter = 100 centimeters

Solution

This problem has at least two solutions. I will show one solution and leave you to look for another solution. Using the area formula, we can calculate the area of the room in square meters. That is,

A = lw = 6(8) = 48.

So, the area of the room is 48 square meters. However, we are looking for the number of tiles that can cover the room and not the area in square meters. Now, the easiest solution is to find the number of tiles that can fit inside 1 square meter. Since the side of a square is 1 meter which is equal to 100 centimeters, it can fit 4 tiles as shown below.

rectangle area

1 square meter contains 16 tiles

Now, four tiles at the side means 1 square meter contains 4(4) = 16 square tiles. Since there are 48 square meters, the number of tiles needed is

16 \times 48 = 768.

Therefore, we need at least 768 square tiles to cover the entire floor.

In the next post, we will continue our discussion about rectangle area problems.

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5 Responses

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