Question
The trim (shaded area) around the edge of a trunk needs to be painted. If the trim is painted all the
way around, what is the surface area to be painted?
(1 point)
5, 216 in.^2
318 in.^2
636 in.^2
1, 400 in.^2
(the front of the box is 36 inches and 28 inches wide and 25 inches tall)
way around, what is the surface area to be painted?
(1 point)
5, 216 in.^2
318 in.^2
636 in.^2
1, 400 in.^2
(the front of the box is 36 inches and 28 inches wide and 25 inches tall)
Answers
GPT-4o mini
To find the surface area of the trim around the edge of the trunk, we need to calculate the surface area of the sides and the top of the trunk that requires paint.
Since we are only looking at the trim area around the edge, we will calculate the perimeter of the top of the trunk and then multiply it by the height of the trunk.
1. **Calculate the perimeter of the top of the trunk**:
The trunk is rectangular with the dimensions given:
- Width = 28 inches
- Length = 36 inches
The perimeter \( P \) can be calculated using the formula for the perimeter of a rectangle:
\[
P = 2 \times (length + width) = 2 \times (36 + 28) = 2 \times 64 = 128 \text{ inches}
\]
2. **Multiply the perimeter by the height**:
The height of the trunk is given as 25 inches. To get the surface area of the trim:
\[
\text{Surface area to be painted} = P \times \text{height} = 128 \text{ in} \times 25 \text{ in} = 3200 \text{ in}^2
\]
However, we might be looking for the area of the trim around the sides only, or possibly the top. Let’s ensure we look specifically for the trim area:
If we need to check if we missed anything key or if the surface area provided fulfills match any options, we can isolate edges depending on what’s given.
Given your options and reviewing the calculations as noticeable, it may suit to just assign an area based on the trim covering rather than the total encasing area.
In terms of specifics based on clarification, the calculation leans toward options that require a close check; it appears the provided area options are far less unless it accounts for sectioned areas closer related to boundary or selective edges.
Sending a query could refine any areas that should be localized or adjusted accordingly based on purpose-critical specifics or area positioning.
Could offer further refinements needed if trim is selective, or check if any overlapping areas are what's intended?
Since we are only looking at the trim area around the edge, we will calculate the perimeter of the top of the trunk and then multiply it by the height of the trunk.
1. **Calculate the perimeter of the top of the trunk**:
The trunk is rectangular with the dimensions given:
- Width = 28 inches
- Length = 36 inches
The perimeter \( P \) can be calculated using the formula for the perimeter of a rectangle:
\[
P = 2 \times (length + width) = 2 \times (36 + 28) = 2 \times 64 = 128 \text{ inches}
\]
2. **Multiply the perimeter by the height**:
The height of the trunk is given as 25 inches. To get the surface area of the trim:
\[
\text{Surface area to be painted} = P \times \text{height} = 128 \text{ in} \times 25 \text{ in} = 3200 \text{ in}^2
\]
However, we might be looking for the area of the trim around the sides only, or possibly the top. Let’s ensure we look specifically for the trim area:
If we need to check if we missed anything key or if the surface area provided fulfills match any options, we can isolate edges depending on what’s given.
Given your options and reviewing the calculations as noticeable, it may suit to just assign an area based on the trim covering rather than the total encasing area.
In terms of specifics based on clarification, the calculation leans toward options that require a close check; it appears the provided area options are far less unless it accounts for sectioned areas closer related to boundary or selective edges.
Sending a query could refine any areas that should be localized or adjusted accordingly based on purpose-critical specifics or area positioning.
Could offer further refinements needed if trim is selective, or check if any overlapping areas are what's intended?