A child and grandfather plan a backyard garden together

The Garden Project

Maya and Grandpa Leo are building a rectangular garden. How much soil covers it? How much fence wraps around it? Math has the answers!

4th Grade Math

Step 1: Cover the Inside

6 feet long

4 feet
wide

The garden is 6 feet long and 4 feet wide. Each square is 1 square foot of soil. The area is the space inside. How many square feet cover the garden?

There are 4 rows with 6 squares in each row. Instead of counting, multiply: 6 × 4 = 24 square feet. That is the area formula: Area = length × width.

Step 2: Walk the Outside Edge

Now Grandpa Leo needs a fence. The fence goes around the outside edge, not inside. That distance is the perimeter.

6 + 4 + 6 + 4 = ?

A rectangle has two lengths and two widths. 6 + 4 + 6 + 4 = 20 feet of fence. A faster way: Perimeter = 2 × (length + width) = 2 × 10 = 20.

Let's Remember

Two Powerful Formulas

          Area = length × width (space inside)

          Perimeter = 2 × (length + width) (edge around)

Area is measured in square units, like square feet. Perimeter is measured in plain units, like feet. Ask yourself: am I covering the inside or wrapping the outside?

Solve It!

A rectangle is 9 cm long and 7 cm wide. Find its area.

9 × 7 = ?

Area = length × width = 9 × 7 = 63 square cm. Careful: 32 is the perimeter, not the area!

Word Problem

A soccer field at Maya's school is 12 meters long and 8 meters wide. The coach wants rope around the whole edge. How much rope does she need?

Rope wraps the edge, so use perimeter: 2 × (12 + 8) = 2 × 20 = 40 meters. 96 is the area, and 20 is only two sides!

Watch Out!

A Common Mistake

          Jade says a 10 by 3 rectangle has a perimeter of 13.

          But 10 + 3 counts only two sides!

Grandpa Leo A rectangle has four sides. You must determine the sum of all of them. The real perimeter is 2 × (10 + 3) = 26. Always double the sum, like folding a paper in half twice!

Find the Missing Factor

A rug has an area of 54 square feet. Its length is 9 feet. The width is a missing factor!

9 × ? = 54

Think: 9 × what = 54? Divide to find it: 54 ÷ 9 = 6. The width is 6 feet, because 9 × 6 = 54.

Word Problem

A rectangular bedroom needs 72 square feet of new flooring. The room is 8 feet long. How wide is the room?

Area = length × width, so 8 × width = 72. Divide: 72 ÷ 8 = 9. The room is 9 feet wide.

Mystery Side

A picture frame has a perimeter of 30 inches. One side is 9 inches. How long is the other side?

2 × (9 + ?) = 30

Half the perimeter is 30 ÷ 2 = 15. That is one length plus one width. So 15 - 9 = 6 inches.

Which Formula Wins?

Nia wants to know how much carpet will cover her rectangular floor. Analyze the situation. What should she find?

Carpet covers the space inside the floor, so Nia needs area: length × width. Perimeter would only measure the baseboard around the wall.

Challenge Round!

A rectangular patio has an area of 48 square meters and a length of 8 meters. First find the width. Then find the perimeter of the patio!

Step 1: width = 48 ÷ 8 = 6 meters. Step 2: perimeter = 2 × (8 + 6) = 2 × 14 = 28 meters. Two steps, one victory!

Think About It

Compare and contrast: when would a builder need perimeter, and when would a painter need area? How are the two measurements different?

Great Work!

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