Question
Abbey is getting new carpet in her living room and hallway. The following diagram shows the two together.
Note: Figure not drawn to scale
If a = 32 ft, b = 15 ft, c = 16 ft, and d = 19 ft, what is the area of the living room and hallway together?
A.
784 ft2
B.
368 ft2
C.
164 ft2
D.
82 ft2
Note: Figure not drawn to scale
If a = 32 ft, b = 15 ft, c = 16 ft, and d = 19 ft, what is the area of the living room and hallway together?
A.
784 ft2
B.
368 ft2
C.
164 ft2
D.
82 ft2
Answers
GPT-4o mini
To find the area of the living room and hallway, we can break it down into two rectangles based on the given dimensions. The fractions a, b, c, and d represent the lengths for the rectangles:
- Living room: Length \( a \) and width \( b \)
- Hallway: Length \( c \) and width \( d \)
The area of a rectangle is calculated using the formula \( \text{Area} = \text{length} \times \text{width} \).
1. Calculate the area of the living room:
\[
\text{Area}_{\text{living room}} = a \times b = 32 \, \text{ft} \times 15 \, \text{ft} = 480 \, \text{ft}^2
\]
2. Calculate the area of the hallway:
\[
\text{Area}_{\text{hallway}} = c \times d = 16 \, \text{ft} \times 19 \, \text{ft} = 304 \, \text{ft}^2
\]
3. Now, add both areas together to find the total area:
\[
\text{Total Area} = \text{Area}_{\text{living room}} + \text{Area}_{\text{hallway}} = 480 \, \text{ft}^2 + 304 \, \text{ft}^2 = 784 \, \text{ft}^2
\]
The total area of the living room and hallway together is \( 784 \, \text{ft}^2 \).
Thus, the correct answer is **A. 784 ft²**.
- Living room: Length \( a \) and width \( b \)
- Hallway: Length \( c \) and width \( d \)
The area of a rectangle is calculated using the formula \( \text{Area} = \text{length} \times \text{width} \).
1. Calculate the area of the living room:
\[
\text{Area}_{\text{living room}} = a \times b = 32 \, \text{ft} \times 15 \, \text{ft} = 480 \, \text{ft}^2
\]
2. Calculate the area of the hallway:
\[
\text{Area}_{\text{hallway}} = c \times d = 16 \, \text{ft} \times 19 \, \text{ft} = 304 \, \text{ft}^2
\]
3. Now, add both areas together to find the total area:
\[
\text{Total Area} = \text{Area}_{\text{living room}} + \text{Area}_{\text{hallway}} = 480 \, \text{ft}^2 + 304 \, \text{ft}^2 = 784 \, \text{ft}^2
\]
The total area of the living room and hallway together is \( 784 \, \text{ft}^2 \).
Thus, the correct answer is **A. 784 ft²**.