9.4 Solve Area Problems

9.4 Solve Area Problems

I can find the area of a rectangular region that is formed by taking away rectangular pieces from its interior.

Step It Out Problem 1

Josh runs a glass-bottom boat touring business. He wants to install a non-slip surface on the walkway of the deck. What is the area of the walkway that needs the non-slip surface?

Multiple Select

What do you know? Select the two correct answers.

• the area of the walkway

• the length and width of the glass

• the weight of the glass

• the length and width of the deck

We know the lengths and widths

In the diagram, the dimensions of the glass and the dimensions of the deck are labeled. You want to find the area of the walkway that needs the non-slip surface.

How can we solve this problem?

• suggestions?

• I can find the area of both rectangles and then subtract the area of the glass from the area of the deck.

Fill in the Blanks

Use the length and width measurements to find the area of the glass.

The area is 48 square feet.

The length of the glass is 12 ft, and the width of the glass is 4 ft.

A = 12 × 4 and 12 × 4 = 48, so the area of the glass is 48 square feet.

Fill in the Blanks

Use the length and width measurements to find the area of the deck.

The area of the deck is 180 square feet.

The length of the deck is 18 ft, and the width of the deck is 10 ft.

A = 18 × 10 and 18 × 10 = 180, so the area of the deck is 180 square feet.

Multiple Choice

Subtract the area of the glass from the area of the deck. Choose the correct answer.

180 − 48 = ?

• 132

• 142

• 148

The area of the walkway that needs the non-slip surface is 132 square feet.

Subtract the area of the glass from the area of the deck.180 – 48 = 132, so the area of the walkway that needs the non-slip surface is 132 square feet.

Step It Out Problem 2

Josh has a second glass-bottom boat with two viewing areas. He wants to install a non-slip surface on the walkway of the deck. What is the area of the walkway that needs the non-slip surface?

Multiple Select

What do you know? Select the three correct answers.

• the area of the walkway

• the weight of Glass A

• the length and width of Glass B

• the length and width of Glass A

• the length and width of the deck

We know the lengths and widths.

In the diagram, the dimensions of Glass A, Glass B, and the deck are all labeled. You want to find the area of the walkway.

How would we solve this problem?

• Suggestions?

• First, I can find the area of all three rectangles.

• Then, I add the areas of the glass.

• Finally, I subtract that sum from the area of the deck.

Fill in the Blanks

Find the area of Glass A.

The area of glass A is 63 square feet.

The length of Glass A is 9 ft, and the width is 7 ft, so A = 9 × 7.

Since 9 × 7 = 63, the area of Glass A is 63 square feet.

Fill in the Blanks

Find the area of Glass B.

The area of Glass B is 99 square feet.

The length of Glass B is 11 ft, and the width is 9 ft, so A = 11 × 9.

Since 11 × 9 = 99, the area of Glass B is 99 square feet.

Fill in the Blanks

Find the area of the Deck.

The area of the deck is 375 square feet.

The length of the deck is 25 ft, and the width is 15 ft, so A = 25 × 15.

Since 25 × 15 = 375, the area of the deck is 375 square feet.

Fill in the Blanks

So if we take 99+63 to find the area of the two glass pieces and subtract that from the deck, which is 375, how much is that?

or

375-99-63=

The area of the walkway that needs the non-slip surface is 213 square feet.

First add the areas of the glass. Then subtract the sum from the area of the deck to find the answer.63 + 99 = 162 and 375 – 162 = 213The area of the walkway that needs the non-slip surface is 213 square feet.