Area of Combined Rectangles

9.1 Apply the Area Formula to Rectangles

I can find the area of a rectangle by using the formula for area.

Open Ended

Making banners is a very old craft. Banners are usually made of cloth and can have a symbol, logo, slogan, or any other message. How can you find the area of each banner?

Each of these banners has the same area!

The area of the first banner is 5 squares down × 8 squares across = 40 squares total. The area of the second banner is 4 squares down × 10 squares across = 40 squares total. Both banners have the same area, 40 square feet.

For the next few questions, we'll be using this image and question.

Sports fans use banners to show support. How can you find the area of the banner?

Multiple Choice

The length of the rectangle is _____ unit squares, and the width is ____ unit squares.

• 7, 4

• 4, 7

• 4, 4

• 7, 7

The length is 7 units and the width is 4 units.

You can count the number of squares along the length and width of the rectangle. The longer side is the length, and the shorter side is the width. The length of the rectangle is 7 unit squares, and the width is 4 unit squares.

Fill in the Blanks

The answer is 28 square units.

When you count the number of unit squares within the rectangle, this is the area. There are 28 unit squares inside the rectangle, so the area is 28 unit squares.

Multiple Choice

What is the relationship between the length and width and the area? Complete the statement.

The _____ the length and width of the rectangle is equal to the area.

• difference between

• sum of

• product of

Area is the product of the length and width.

When you multiply the length and the width of a rectangle, you find the product. The product of the length and width is equal to the area.

You can also write the formula for the area (A) of a rectangle as A = b × h.

• Think of the base (b) of a rectangle as the measure of any side.

• The height (h) of the rectangle is the measure of a side perpendicular to the base.

• The perpendicular line is a line that crosses another line at a 90° angle.

Our next problem deals with the following image and question:

The Hawks' fans are making a giant banner for a competition. The banner has the dimensions shown. What is the area of the banner?

Multiple Choice

Pick the correct formula to find the area of this rectangle.

• A = 5 x 7

• A = 5 x 11

• A = 7 x 11

Multiple Choice

So what does A equal in A = 5 x 7

• 30

• 32

• 35

• 55

• 77

The area is 35 square meters.

7 × 5 = 35, so the area of the banner is 35 square meters.