Perimeter and Area

Free sample questions, a clear explanation, and 5 practice skills with an AI tutor that guides without giving the answer away.

Concept Review

Perimeter: Building the Perfect Fence

Imagine you want to build a fence around your rectangular backyard. How much fencing would you need to buy? You'd need to measure all the way around the outside edge — that's called the perimeter.

Perimeter is the distance around the outside of any shape. For rectangles, we have a special shortcut that makes measuring super easy because rectangles have a secret: opposite sides are always exactly the same length.

The Rectangle Perimeter Formula

Instead of measuring all four sides separately, we can use this powerful formula:

Perimeter = 2 × length + 2 × width

P = 2l + 2w

Let's see this formula in action! Say your backyard is 12 feet long and 8 feet wide. Here's how much fencing you'd need:

🔨 Building Our Fence

Length: 12 feet (this appears twice — top and bottom)
Width: 8 feet (this appears twice — left and right)

Using our formula:

P = 2 × 12 + 2 × 8

P = 24 + 16

P = 40 feet

🔑 The "Double Everything" Trick

Here's the cool part: you can also think of perimeter as doubling the sum of length and width!

P = 2 × (length + width)

For our backyard: P = 2 × (12 + 8) = 2 × 20 = 40 feet. Same answer, different path!

Why This Formula Works

Think about walking around that rectangular fence. You'd walk 12 feet across the back, 8 feet down the side, 12 feet across the front, and 8 feet up the other side. You walked the length twice and the width twice — exactly what our formula does!

🎯 Key Takeaway

Whether you're planning a fence, figuring out how much ribbon you need for a picture frame, or measuring a soccer field, the rectangle perimeter formula P = 2l + 2w gives you the exact distance around any rectangular shape. Math helps you plan the real world!

Sample questions

1. What is the perimeter of a rectangle with a length of 8 cm and a width of 5 cm?

○ 13 cm

✓ 26 cm

○ 40 cm

○ 20 cm

Answer: 26 cm — Perimeter is the distance around. $(8 + 5) imes 2 = 26$.

2. A square garden has sides that are 10 meters long. What is its perimeter?

○ 100 meters

○ 20 meters

✓ 40 meters

○ 10 meters

Answer: 40 meters — For a square, multiply the side by 4: $10 imes 4 = 40$.

3. If the perimeter of a rectangle is 20 cm and the length is 6 cm, what is the width?

○ 14 cm

○ 8 cm

○ 10 cm

✓ 4 cm

Answer: 4 cm — Subtract the two lengths from the total: $20 - 12 = 8$. Then divide by 2 to find the width: 4 cm.

Skills in this topic

Find the perimeter of a rectangle using a formula
Find the area of a rectangle using the standard formula
Find the area and perimeter of complex (rectilinear) shapes
Compare perimeter and area of different shapes
Solve real-world word problems involving area and perimeter

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