Question
What is the surface area of the triangular prism?
A triangular prism. The rectangular sides are 8 feet by 2.5 feet, 8 feet by 6 feet, and 8 feet by 6.5 feet. The triangular sides have a base of 2.5 feet and height of 6 feet.
[Not drawn to scale]
115 square feet
120 square feet
135 square feet
150 square feet
A triangular prism. The rectangular sides are 8 feet by 2.5 feet, 8 feet by 6 feet, and 8 feet by 6.5 feet. The triangular sides have a base of 2.5 feet and height of 6 feet.
[Not drawn to scale]
115 square feet
120 square feet
135 square feet
150 square feet
Answers
Answered by
GPT-4o mini
To find the surface area of the triangular prism, we need to calculate the areas of its two triangular bases and its three rectangular sides.
1. **Calculate the area of the triangular base**:
The area \(A\) of a triangle can be calculated using the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
For this triangular base, the base is 2.5 feet and the height is 6 feet:
\[
A = \frac{1}{2} \times 2.5 \times 6 = \frac{1}{2} \times 15 = 7.5 \text{ square feet}
\]
Since there are two identical triangular bases, the total area for both is:
\[
\text{Total triangular area} = 2 \times 7.5 = 15 \text{ square feet}
\]
2. **Calculate the areas of the rectangular sides**:
We have three rectangular sides with the following dimensions:
- First rectangular side: \(8 \text{ feet} \times 2.5 \text{ feet}\)
- Second rectangular side: \(8 \text{ feet} \times 6 \text{ feet}\)
- Third rectangular side: \(8 \text{ feet} \times 6.5 \text{ feet}\)
Now we will calculate the area of each rectangular side:
- Area of the first rectangular side:
\[
A_1 = 8 \times 2.5 = 20 \text{ square feet}
\]
- Area of the second rectangular side:
\[
A_2 = 8 \times 6 = 48 \text{ square feet}
\]
- Area of the third rectangular side:
\[
A_3 = 8 \times 6.5 = 52 \text{ square feet}
\]
Now, calculate the total area of the three rectangular sides:
\[
\text{Total rectangular area} = A_1 + A_2 + A_3 = 20 + 48 + 52 = 120 \text{ square feet}
\]
3. **Calculate the total surface area of the triangular prism**:
Finally, we add the total area of the triangular bases to the total area of the rectangular sides:
\[
\text{Total surface area} = \text{Total triangular area} + \text{Total rectangular area} = 15 + 120 = 135 \text{ square feet}
\]
So, the surface area of the triangular prism is \(\boxed{135} \text{ square feet}\).
1. **Calculate the area of the triangular base**:
The area \(A\) of a triangle can be calculated using the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
For this triangular base, the base is 2.5 feet and the height is 6 feet:
\[
A = \frac{1}{2} \times 2.5 \times 6 = \frac{1}{2} \times 15 = 7.5 \text{ square feet}
\]
Since there are two identical triangular bases, the total area for both is:
\[
\text{Total triangular area} = 2 \times 7.5 = 15 \text{ square feet}
\]
2. **Calculate the areas of the rectangular sides**:
We have three rectangular sides with the following dimensions:
- First rectangular side: \(8 \text{ feet} \times 2.5 \text{ feet}\)
- Second rectangular side: \(8 \text{ feet} \times 6 \text{ feet}\)
- Third rectangular side: \(8 \text{ feet} \times 6.5 \text{ feet}\)
Now we will calculate the area of each rectangular side:
- Area of the first rectangular side:
\[
A_1 = 8 \times 2.5 = 20 \text{ square feet}
\]
- Area of the second rectangular side:
\[
A_2 = 8 \times 6 = 48 \text{ square feet}
\]
- Area of the third rectangular side:
\[
A_3 = 8 \times 6.5 = 52 \text{ square feet}
\]
Now, calculate the total area of the three rectangular sides:
\[
\text{Total rectangular area} = A_1 + A_2 + A_3 = 20 + 48 + 52 = 120 \text{ square feet}
\]
3. **Calculate the total surface area of the triangular prism**:
Finally, we add the total area of the triangular bases to the total area of the rectangular sides:
\[
\text{Total surface area} = \text{Total triangular area} + \text{Total rectangular area} = 15 + 120 = 135 \text{ square feet}
\]
So, the surface area of the triangular prism is \(\boxed{135} \text{ square feet}\).