Interactive Activity

As American settlers moved to the dry climate of the desert southwest, they built small rectangular prism dwellings called adobe houses. The Gachado Well Line Camp adobe house in Organ Pipe Cactus National Monument in Arizona is an example of an adobe house. The front face of the dwelling is a rectangle with cut-outs for the door and window. The door is a rectangle and the window is a square.

The front face of the house is 20 feet wide and 8 feet high.

The door is 2 1 over 2 1 2 feet wide and 6 feet tall.

The window has edge lengths that are 1 3 over 4 3 4 feet.

What is the area of the front face of the adobe house, excluding the cut-outs for the door and window?

The dimensions of the parts of the front face of the house are:

Front face: width = 20 feet and height = 8 feet

Door: width = 2 1 over 2 1 2 feet and height = 6 feet

Window: side length = 1 3 over 4 3 4 feet

What does the problem ask for?

The problem asks for the area of the front face without the door and window.

Step 2: Make a plan.

What is your plan to solve this problem?

Laura's Plan

The front face is a rectangle, so I will use the area formula for a rectangle, A = bh, to calculate the area of the front face. I will also need to subtract the area of the door, which is also a rectangle, and the window, which is a square.

What area formulas do you need to use?

Use the area formula for a rectangle, A = bh

for all three figures since a square is a special type of rectangle.

Step 1: Understand the problem.

Write an equation that you could use to calculate the area of each figure: the front face, the door, and the window.

Front face: A = (20 ft)(8 ft)

Door: A = (2 1 over 2 1 2 ft)(6 ft)

Window: A = (1 3 over 4 3 4 ft)(1 3 over 4 3 4 ft)

Step 3: Implement the plan.

Area of front face:

A = (20 ft)(8 ft)

= 160 ft²

Area of door:

A = (2 1 over 2 1 2 ft)(6 ft)

= 15 ft²

Area of window:

A = (1 3 over 4 3 4 ft)(1 3 over 4 3 4 ft)

= 3 1 over 16 1 16 ft²

Area of front face - door - window:

A = 160 ft² - 15 ft² - 3 1 over 16 1 16 ft²

A = 141 15 over 16 15 16 ft²

Step 4: Check your answer for reasonableness.

Strategy check: Use rounding to estimate your answer.
Round 2 1 over 2 1 2 feet and 1 3 over 4 3 4 feet to the nearest foot.

2 1 over 2 1 2 feet → 3 feet

1 3 over 4 3 4 feet → 2 feet

Use the rounded values to estimate the area of the front face, the door, and the window.

Area of front face: A = (20 ft)(8 ft) = 160 ft²

Area of door: A ≈ (3 ft)(6 ft) = 18 ft²

Area of window: A ≈ (2 ft)(2 ft) = 4 ft²

A ≈ 160 ft² - 18 ft² - 4 ft²

A ≈ 138 ft²

Compare your estimate to your actual answer.

The estimate of 138 ft² is close to the actual answer of

141 15 over 16 15 16 ft², so the answer is reasonable.