Perimeter of a Rectangle - Mixed Number Dimensions

🔑 Key Concepts

• Perimeter is the total distance around a figure.
• For a rectangle, opposite sides are equal in length.
• You can find the perimeter of a rectangle by adding all four side lengths.
• You can also use the shortcut formula \( P = 2l + 2w \).
• Mixed numbers can be added by combining whole numbers and fractional parts carefully.

✏️ Worked Example — Finding the Perimeter of a Rectangle

Example — Add All Four Sides of the Rectangle

Let’s find the perimeter of the rectangle shown below.

The image shows a rectangle with a length of \( 6\frac{1}{2}\text{ cm} \) and a width of \( 3\frac{1}{2}\text{ cm} \). Since opposite sides of a rectangle are equal, the four side lengths are:

\( 6\frac{1}{2},\ 6\frac{1}{2},\ 3\frac{1}{2},\ 3\frac{1}{2} \)

We can use the perimeter formula:

\( P = 2l + 2w \)

Substitute the given values:

\( P = 2\left(6\frac{1}{2}\right) + 2\left(3\frac{1}{2}\right) \)

Multiply each dimension by 2. This makes sense because each measurement appears twice in a rectangle.

\( P = 13 + 7 \)

Now add the two results:

\( P = 20 \)

We can also check by adding all four sides directly:

\( P = 6\frac{1}{2} + 6\frac{1}{2} + 3\frac{1}{2} + 3\frac{1}{2} \)

\( P = 13 + 7 \)

\( P = 20\text{ cm} \)

🧠 Math Vocabulary

• Perimeter: The total distance around a figure.
• Rectangle: A four-sided figure with opposite sides equal and four right angles.
• Length: The longer side of a rectangle.
• Width: The shorter side of a rectangle.
• Mixed number: A number made of a whole number and a fraction.

💡 Main Idea

To find the perimeter of a rectangle, add all four sides. Because opposite sides of a rectangle are equal, you can also use the shortcut formula \( P = 2l + 2w \). Both methods give the same result.

📚 What You Should Already Know

Before working on perimeter of rectangles, students should be comfortable adding whole numbers and mixed numbers, and they should know that opposite sides of a rectangle have the same length.

🚀 What Comes Next

After learning perimeter of rectangles, students can move on to finding perimeter of irregular figures, working with mixed-number side lengths, and solving word problems involving distance around shapes.

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