Don’t be a square (at least not all the time). Learn all about rectangles.

Author

Taylor Hartley

Expert Reviewer

Jill Padfield

Published: August 24, 2023

Don’t be a square (at least not all the time). Learn all about rectangles.

Author

Taylor Hartley

Expert Reviewer

Jill Padfield

Published: August 24, 2023

Rectangles

Don’t be a square (at least not all the time). Learn all about rectangles.

Author

Taylor Hartley

Expert Reviewer

Jill Padfield

Published: August 24, 2023

Key takeaways

**A rectangle is a four-sided closed shape with equal parallel sides**– A square is always a rectangle, but a rectangle is not always a square!**There are three main parts to a rectangle shape**– A rectangle’s length, width, and diagonal are important when calculating different measurements.**Follow simple equations to calculate the perimeter and area of a rectangle**– It’s not too hard to figure out how much space a rectangle takes up, so long as you know your length and width.

We know our world is made up of all different shapes and sizes. One of the most common shapes out there is the rectangle! Rectangles share a lot of qualities similar to the square, but they’re not exactly alike.

Let’s learn all about rectangles: what they are, what sets them apart from their square siblings, and what to do when you’re trying to measure one!

Like a square, a rectangle is a two-dimensional (or flat) shape with four sides and four right angles. By a rectangle’s definition, opposite sides must be equal and parallel to each other.

The two dimensions of a rectangle are length and width. Length is the longer side of a rectangle, while width is the shorter side of the rectangle.

**Did you know?** A square IS a rectangle. It has four sides, four right angles, and the opposite sides are equal and parallel. BUT, not all rectangles are squares because they might not have sides that are equal to each other.

Take a look around you, and you will find rectangles everywhere! Need a few examples? Let’s take a look at some real-life rectangles.

Rectangles have a few different names, which can be confusing if you don’t know what they mean. Let’s take a quick look at other names for rectangles so you can be in the know.

**Equiangular quadrilateral**– Equiangular means equal angles, and quadrilateral means four sides. A rectangle is an equiangular quadrilateral since it is a 4-sided closed shape with equal angles!**Right-angled parallelogram**– A parallelogram is a quadrilateral with equal and parallel sides, and a rectangle is a special parallelogram because it has right angles.

There are a few qualities a shape must have to be considered a rectangle. The shape must be a flat, closed shape with:

- 4 sides, 4 angles, and 4 corners (also known as vertices)
- 2 dimensions (length and width)
- 4 angles that measure 90 degrees
- 4 opposite sides that are equal and parallel
- 2 diagonals of equal length

Like circles and squares, there are different parts to a rectangle. Understanding these parts will help you calculate the perimeter and area.

This is pretty simple: the length of a rectangle is how long a rectangle is. You can find the length by measuring one of the long sides of the rectangle. If one long side is not equal to the other long side, it is **not** a rectangle.

The width of a rectangle is how wide the rectangle is. You can find the width by measuring one of the two short sides of the rectangle. Like with length, if one of the short sides does not equal the other short side, it is **not** a rectangle.

Diagonals are the line segments that connect the opposite corners of the rectangle. Diagonals should be equal to each other.

There’s plenty we can calculate using the parts of a rectangle. If we have the length and width, we can calculate the perimeter and the area. We can also use the length and width to calculate the length of the diagonal, but we will have to use an equation called the Pythagorean theorem.

Let’s go from easiest to hardest: measuring perimeter.

The perimeter is the measure of the outside of a rectangle. Put plainly, you can calculate the perimeter like this:

**length + width + length + width = perimeter**

Or, if you know how to multiply:

**2(length) + 2(width) = perimeter**

**You can also write this as: (length + width) × 2 = perimeter**

So, let’s find the perimeter of the rectangle we’ve been working with:

You can write this out either as

**3 + 1 + 3 + 1** or

**2(3) + 2(1)** or

**(3+1) × 2**

Do your calculations, and you should find that the perimeter is 8 inches.

The area measures the inside of the rectangle or how much space it takes up. Calculating the area of a rectangle is pretty easy, as long as you can multiply!

Multiply the length by the width to find the area.

Put another way: length × width = area

Let’s find the area of our rectangle.

This means that the area is 3 × 1 = 3 inches.

Finding the length of diagonals using the length and width of the sides is a little more complicated. We have to use what’s known as the Pythagorean theorem, which you may not learn until 6th grade or later.

Let’s talk about how to do it, just in case you want to challenge yourself.

The diagonal of a rectangle is the hypotenuse, or the slanted side of a right triangle. It’s called a right triangle because it has a 90-degree angle at its base.

**How do you calculate the hypotenuse of a right triangle? **

The Pythagorean Theorem is as follows:

**A2 + B2 = C2**

A = length, B = width, and C = the length of the diagonal or the triangle’s hypotenuse.

The small 2 next to each letter means we need to **square** the number or multiply it by itself. So, using our example rectangle:

**3 × 3 = 9**

**1 × 1 = 1**

**C = We don’t know, right? **

**So 9+1 = 10**

**10 = C2**

So, to find C on its own, we take the square root of both sides, which is the opposite of squaring.

The diagonal is equal to the square root of 10, which can be written as √10.

If you know how to calculate decimals, this is equal to **3.162**.

Now that we know what a rectangle is and how to find the perimeter and the area, let’s practice together! We’re going to walk through the next three practice problems with you.

**1. Which of the following is a rectangle?**

**D** has equal, opposite sides that are parallel and four 90-degree angles, so **D** is the correct answer.

**2. Using the rectangle above, calculate the perimeter. **

So we know that if the top side of the rectangle is 3 inches, so is the bottom side. Additionally, since the right side of the rectangle is 2 inches, we know that the left side is also 2 inches.

That means the perimeter equals 3 + 2 + 3 + 2, or 2(3) + 2(2), or (3+2) × 2

If we add these sides together or multiply each side by 2, we’ll find out that the perimeter is **10 inches**.

**3. Using the rectangle above, calculate the area. **

Remember, the area of a rectangle can be calculated by multiplying the length by the width. So:

3 × 2 = **6 inches**

Ready to give it a go?

You’ve learned valuable skills about rectangles. Now it’s time to put your skills to the test! Take a look at these practice problems and find the right answer on your own.

*Click to reveal the answer.*

Both **A** and **B** are rectangles

The answer is B, **False**.

The answer is A, **Yes**.

For the last two questions, use the figure below:

The answer is **16 cm**

The answer is **12 cm**

Both A and B are rectangles.

**How did we get here? **

- Remember, rectangles must:
- Have 4 sides
- And each opposite side must be equal and parallel
- With 90-degree angles

- So, looking at the shapes, we can determine that the square (A) and the rectangle (B) are BOTH rectangles.

The answer is B, **False.** A square is ALWAYS a rectangle, but a rectangle is not always a square.

The answer is A, yes. It is a square, and a square matches all qualities of a rectangle!

The answer is **16 cm**.

**How did we get here?**

- Let’s identify the two measurements we need: the length and the width.
- The length is 6 cm and the width is 2 cm.
- So now, let’s use our perimeter equation: 2(6) + 2(2) = 16 cm.

The answer is **12 cm**.

**How did we get here?**

- Let’s identify the two measurements we need: the length and the width.
- The length is 6 cm and the width is 2 cm.
- So now, let’s use our area equation: 6 × 2 =
**12 cm**.

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We understand that diving into new information can sometimes be overwhelming, and questions often arise. That’s why we’ve meticulously crafted these FAQs, based on real questions from students and parents. We’ve got you covered!

A rectangle must have 4 sides and 4 right angles. It has two pairs of parallel and opposite sides, too. The parallel and opposite sides must equal each other.

Other names for rectangles include equilateral quadrilateral and right-angled parallelogram.

To calculate the area of a rectangle, you simply measure its length by its width. So, if you have a rectangle with a length of 4 cm and a width of 2 cm, you multiply 4 by 2 to get 8 cm.

All squares are rectangles, but not all rectangles are squares! Because a square follows the properties of a rectangle, it must be considered a rectangle.

However, rectangles do not have to have 4 equal sides to be called rectangles.

To calculate the perimeter of a rectangle, you will add up all four of its sides.

So if you have a rectangle with a length of 5 cm and a width of 2 cm, you would add 5 + 5 + 2 + 2 (or multiply 5 by 2, since you have 2 sides that measure 5 cm, and 2 by 2 since you have 2 sides that measure 2 cm) to get 14 cm.

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Lesson credits

Taylor Hartley

Taylor Hartley is an author and an English teacher based in Charlotte, North Carolina. When she's not writing, you can find her on the rowing machine or lost in a good novel.

Jill Padfield

Jill Padfield has 7 years of experience teaching high school mathematics, ranging from Alegra 1 to AP Calculas. She is currently working as a Business Analyst, working to improve services for Veterans while earning a masters degree in business administration.

Taylor Hartley

Taylor Hartley is an author and an English teacher based in Charlotte, North Carolina. When she's not writing, you can find her on the rowing machine or lost in a good novel.

Jill Padfield

Jill Padfield has 7 years of experience teaching high school mathematics, ranging from Alegra 1 to AP Calculas. She is currently working as a Business Analyst, working to improve services for Veterans while earning a masters degree in business administration.

Parents, sign up for a DoodleMath subscription and see your child become a math wizard!

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