Math Core

Many rooms, gardens and playgrounds are not simple rectangles. They are shaped like an L, a T or a U. You can still find their area: break the shape into rectangles, find each area, and add.

Break it into rectangles

Here is an L-shaped figure made of unit squares.

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You can't use one multiplication for the whole shape, because the rows are not all the same length. But you can split it into two rectangles:

The top part is 3 rows of 2: $3 \times 2 = 6$ .
The bottom part is 2 rows of 6: $2 \times 6 = 12$ .

Add the parts: $6 + 12 = 18$ . The area is 18 square units. Count the squares to check: there are 18.

Area adds up

To find the area of a shape made of rectangles:

Split the shape into rectangles that don't overlap.
Find the area of each rectangle.
Add the areas.

Finding the side lengths

Here is the same L shape drawn with side lengths.

An L shape. Bottom side: 6. Right side: 2. Left side: 5. Top side: 2.

Sometimes a side length is not written, and you must figure it out. The left side is 5 tall, and the bottom part is 2 tall. So the top part is $5 - 2 = 3$ tall. The bottom is 6 long, and the top part is 2 wide, so the step on the right is $6 - 2 = 4$ long.

There is often more than one way to split. Both ways give the same area.

Worked example: Two ways to split

Find the area of the L shape above.

Way 1: cut across. Bottom rectangle: $6 \times 2 = 12$ . Top rectangle: $2 \times 3 = 6$ . Total: $12 + 6 = 18$ .

Way 2: cut down. Left rectangle: $2 \times 5 = 10$ . Right rectangle: $4 \times 2 = 8$ . Total: $10 + 8 = 18$ .

Either way, the area is 18 square units.

Worked example: A room with a closet

A bedroom is a rectangle 8 feet by 7 feet. A closet that is 3 feet by 2 feet sticks out from one wall. What is the total floor area?

Bedroom: $8 \times 7 = 56$ square feet.
Closet: $3 \times 2 = 6$ square feet.

Total: $56 + 6 = 62$ . The floor area is 62 square feet.

Take away a missing piece

Sometimes it is easier to start with a big rectangle and subtract the part that is missing.

A U shape. The full shape is 6 wide and 4 tall. A notch 2 wide and 3 deep is cut out of the top middle.

Worked example: Subtract the notch

Find the area of the U shape.

The big rectangle would be $6 \times 4 = 24$ square units. The notch is $2 \times 3 = 6$ square units.

$24 - 6 = 18$ . The area is 18 square units.

Check by adding instead: the bottom strip is $6 \times 1 = 6$ , and each side post is $2 \times 3 = 6$ . $6 + 6 + 6 = 18$ .

Common mistake

Don't let your rectangles overlap. If two parts share the same squares, those squares get counted twice and your area will be too big. Each square should belong to exactly one rectangle.

Tip

Solve it two different ways. If the answers match, you can be confident you are right.

Practice

Practice 1

Each 🟦 is 1 square unit. What is the area, in square units?

🟦🟦🟦🟦🟦🟦
🟦🟦🟦🟦🟦🟦
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Type a number.

Practice 2

Find the area of this shape, in square units.

A 5 by 2 rectangle along the bottom, with a 3 wide by 4 tall rectangle standing on its left end.

Type a number.

Practice 3

An L shape is split into two rectangles: one is 4 by 3 and the other is 2 by 5. Which shows how to find the total area?

Practice 4

A garden has two rectangular beds that touch but don't overlap. One bed is 4 feet by 4 feet. The other is 6 feet by 3 feet. What is the total area, in square feet?

Type a number.

Practice 5

A rectangle is 7 units by 6 units. A 2 by 3 rectangle is cut out of one corner. What is the area of the shape that is left, in square units?

Type a number.

Practice 6

A classroom is a rectangle 8 meters by 5 meters. A reading nook, 2 meters by 3 meters, is attached to one side. What is the total floor area, in square meters?

Type a number.

Practice 7

An L shape has a left side 7 units tall. It is made of a bottom rectangle 4 units tall and a top rectangle stacked on it. How tall is the top rectangle, in units?

Type a number.

Practice 8

A park is shaped like a rectangle 9 yards by 7 yards with a 3 yard by 4 yard corner missing, where a building stands. What is the area of the park, in square yards?

Type a number.