Question

1. you can find the total area of the house by multiplying the length and width.

which expression represents the area?
8(20 + 4) 20 · 4 + 8
8 · 20 · 4 20(8 + 4)
(image: a rectangle labeled 20 ft (length) and 8 ft (width) with some furniture inside)

Explanation:

Step1: Recall Area of Rectangle

The area of a rectangle is \( \text{length} \times \text{width} \). From the diagram, we need to determine the correct length and width. Wait, maybe there's a misinterpretation. Wait, the problem says "multiplying the length and width". Wait, maybe the total width is \( 8 + 4 \)? Wait, no, looking at the options, let's re-express. Wait, the diagram has 20 ft (maybe length) and 8 ft, but maybe the width is \( 8 + 4 \)? Wait, no, the options: let's check each.

Wait, the area of a rectangle is length × width. Let's see the options:

1. \( 8(20 + 4) \): If length is \( 20 + 4 \) and width is 8.
2. \( 20 \cdot 4 + 8 \): This is not a rectangle area formula.
3. \( 8 \cdot 20 \cdot 4 \): This is volume, not area.
4. \( 20(8 + 4) \): If length is 20 and width is \( 8 + 4 \).

Wait, maybe the diagram's total width is \( 8 + 4 \)? Wait, no, the original problem says "multiplying the length and width". Wait, maybe the length is 20 and the width is \( 8 + 4 \), so area is \( 20 \times (8 + 4) \), which is \( 20(8 + 4) \). Wait, but let's check again. Wait, maybe the length is \( 20 \) and the width is \( 8 + 4 \), so area is \( 20 \times (8 + 4) \), which is option 4. Wait, but let's verify the options.

Wait, the first option is \( 8(20 + 4) \), which would be width 8 and length \( 20 + 4 \). The fourth option is \( 20(8 + 4) \), width \( 8 + 4 \) and length 20. Which is correct? Wait, the diagram shows 20 ft (maybe horizontal length) and 8 ft (vertical), but maybe there's a 4 ft addition? Wait, the problem says "multiplying the length and width". Let's think again.

Wait, the area of a rectangle is \( l \times w \). Let's check each option:

• \( 8(20 + 4) \): Distribute, \( 8 \times 20 + 8 \times 4 \), which is area of two rectangles: 8x20 and 8x4.
• \( 20(8 + 4) \): Distribute, \( 20 \times 8 + 20 \times 4 \), area of two rectangles: 20x8 and 20x4.

Wait, maybe the total width is \( 8 + 4 \), so length 20, width \( 8 + 4 \), so area \( 20(8 + 4) \). So the correct expression is \( 20(8 + 4) \)? Wait, no, wait the diagram: the vertical side is 8 ft, and maybe the horizontal is 20 ft, but there's a 4 ft? Wait, maybe I made a mistake. Wait, let's re-express the problem.

Wait, the problem says "You can find the total area of the house by multiplying the length and width." So length × width. Let's check the options:

• \( 8(20 + 4) \): length = 20 + 4, width = 8.
• \( 20 \cdot 4 + 8 \): Not length × width.
• \( 8 \cdot 20 \cdot 4 \): Not area.
• \( 20(8 + 4) \): length = 20, width = 8 + 4.

Which makes sense? If the width is 8 + 4, then length 20, so area 20(8+4). So the correct expression is \( 20(8 + 4) \), which is the fourth option. Wait, but let's check again. Wait, maybe the length is 20 and the width is 8 + 4, so 20(8+4). So the answer is \( 20(8 + 4) \), which is the last option.

Step2: Verify Each Option

• Option 1: \( 8(20 + 4) \) – If width is 8 and length is 20+4, but does the diagram support that? The diagram has 20 ft (horizontal) and 8 ft (vertical), maybe 4 ft is vertical? No, 8 ft is vertical. So maybe length is 20, width is 8 + 4, so 20*(8+4).
• Option 2: \( 20 \cdot 4 + 8 \) – Not a rectangle area (mixes multiplication and addition incorrectly).
• Option 3: \( 8 \cdot 20 \cdot 4 \) – Volume (three dimensions), not area.
• Option 4: \( 20(8 + 4) \) – Length 20, width 8 + 4, so area is length × width. This matches the formula.

Answer:

\( 20(8 + 4) \) (the fourth option, \( 20(8 + 4) \))