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Word Problems: Area and Perimeter of a Rectangle

In geometry, calculating the area and perimeter of rectangles is typically one of the first lessons we learn. While some of us may find this concept easy, it's worth noting that these skills have real-world applications. Math is not solely for theoretical problem-solving on paper; it can also help us gain valuable insights about the world around us. We will explore how to solve word problems related to finding the area and perimeter of a rectangle.

Review: What is a rectangle?

As you might recall, a rectangle is a parallelogram with four right angles. While a rectangle falls into the general category of a parallelogram, not all parallelograms are rectangles. Interestingly enough, squares are also considered rectangles -- but not all rectangles are squares. This is what a typical rectangle looks like:

Review: Finding the perimeter and area of a rectangle

Let's quickly review how to find the perimeter of a rectangle.

As we may recall, the formula for finding the perimeter is quite simple: $P=2l+2w$ where P is the perimeter, l is the length, and w is the width.

We may also recall that the formula for area is $A=lw$

Things really start to get tricky when we are only given certain values, and we need to find the missing values. These questions can be more difficult than they seem at first.

Solving word problems

Now we're ready to start solving some word problems with our knowledge of rectangle perimeter and area:

Let's assume that we have a swimming pool with a perimeter of 56 meters. We also know that the length of the pool is 16 meters. Can we use these values to determine the width of our pool?

Let's start by visualizing the problem:

Next, let's remind ourselves of the formula for perimeter: P = 2l+2w

Now let's plug in our known values: $formula=2\left(16\right)+2w$

Now we can simplify: $\mathrm{formula56}=32+2w$

Next, we can simplify even further by subtracting 32 from both sides: $f=\frac{axb}{cxd}$

Now all we need to do is ask ourselves what value equals 24 when multiplied by two. In other words, we need to divide both sides of the equation by 2. We are left with: $w=12$

The width of this pool must be 12 meters.

Let's try another question:

Let's say we have a rectangular fence. We know that this fence encloses an area of 500 square feet. We also know that the width of this fenced enclosure is 20 feet. Using these values, can we determine the length of the fence?

First, let's visualize the problem:

Next, let's remind ourselves of the formula for the area of a rectangle: $A=lw$

Now, let's plug in our values: $f=\frac{l}{t}$

Now all that we need to do is divide each side of the equation by 20 to isolate and determine the length $f=\frac{25}{}$.

In other words, the length of our rectangular fenced enclosure is 25 feet.

Rectangle

Word Problems

Perimeter

Flashcards covering the Word Problems: Area and Perimeter of a Rectangle

Common Core: 4th Grade Math Flashcards

Practice tests covering the Word Problems: Area and Perimeter of a Rectangle

Common Core: 4th Grade Math Diagnostic Tests