Question
What is the suriace area uf the triangular prism? square centimeters
Ask by Mills Harrington. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
To find the surface area of a triangular prism in square centimeters, use the formula:
\[
\text{Surface Area} = 2 \times (\text{Area of the triangular base}) + (\text{Perimeter of the triangular base}) \times (\text{Length of the prism})
\]
First, calculate the area of the triangular base using \( \frac{1}{2} \times \text{base} \times \text{height} \). Then, find the perimeter by adding the lengths of all three sides of the triangle. Multiply the perimeter by the length of the prism and add twice the area of the base to get the total surface area.
For example, if the triangular base has sides of 3 cm, 4 cm, and 5 cm, and the height is 2.4 cm, with a prism length of 10 cm:
1. **Area of the base**: \( \frac{1}{2} \times 4 \times 2.4 = 4.8 \, \text{cm}^2 \)
2. **Perimeter**: \( 3 + 4 + 5 = 12 \, \text{cm} \)
3. **Surface Area**: \( 2 \times 4.8 + 12 \times 10 = 9.6 + 120 = 129.6 \, \text{cm}^2 \)
So, the surface area is \( 129.6 \, \text{cm}^2 \).
Solution
It seems like there might be a typo in your question. I'm assuming you're asking for the **surface area of a triangular prism** measured in square centimeters. To help you calculate the surface area, I'll provide the general formula and explain the necessary components.
### Surface Area Formula for a Triangular Prism
The surface area \( (SA) \) of a triangular prism can be calculated using the following formula:
\[
SA = 2 \times \text{Area of the triangular base} + \text{Perimeter of the triangular base} \times \text{Length of the prism}
\]
### Components You Need
1. **Area of the Triangular Base (\( A \))**:
- For a triangle with base \( b \) and height \( h \):
\[
A = \frac{1}{2} \times b \times h
\]
2. **Perimeter of the Triangular Base (\( P \))**:
- If the triangle has sides of lengths \( a \), \( b \), and \( c \):
\[
P = a + b + c
\]
3. **Length of the Prism (\( L \))**:
- This is the distance between the two triangular bases.
### Step-by-Step Calculation
1. **Calculate the Area of One Triangular Base**:
\[
A = \frac{1}{2} \times b \times h
\]
2. **Calculate the Perimeter of the Triangular Base**:
\[
P = a + b + c
\]
3. **Multiply the Perimeter by the Length of the Prism**:
\[
P \times L
\]
4. **Add Twice the Area of the Triangular Base to This Product**:
\[
SA = 2A + P \times L
\]
### Example
Suppose you have a triangular prism with the following dimensions:
- Side lengths of the triangular base: \( a = 3 \, \text{cm} \), \( b = 4 \, \text{cm} \), \( c = 5 \, \text{cm} \)
- Height of the triangular base: \( h = 2.4 \, \text{cm} \) (corresponding to side \( b = 4 \, \text{cm} \))
- Length of the prism: \( L = 10 \, \text{cm} \)
**Steps**:
1. **Area of One Triangular Base**:
\[
A = \frac{1}{2} \times 4 \, \text{cm} \times 2.4 \, \text{cm} = 4.8 \, \text{cm}^2
\]
2. **Perimeter of the Triangular Base**:
\[
P = 3 \, \text{cm} + 4 \, \text{cm} + 5 \, \text{cm} = 12 \, \text{cm}
\]
3. **Surface Area**:
\[
SA = 2 \times 4.8 \, \text{cm}^2 + 12 \, \text{cm} \times 10 \, \text{cm} = 9.6 \, \text{cm}^2 + 120 \, \text{cm}^2 = 129.6 \, \text{cm}^2
\]
**Total Surface Area**: \( 129.6 \, \text{cm}^2 \)
### Conclusion
To calculate the surface area of a triangular prism, you'll need the dimensions of the triangular base (sides and height) and the length of the prism. Once you have these measurements, you can apply the formula as shown above to find the surface area in square centimeters.
If you provide the specific dimensions of your triangular prism, I can help you calculate its exact surface area!
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the surface area of a triangular prism, you'll need to calculate both the area of the triangular bases and the area of the rectangular faces. The surface area formula is: SA = (base area x 2) + (perimeter of base x height). Just remember, always double-check your base measurements to avoid unpleasant surprises like a miscalculated pizza slice! Triangular prisms can be seen everywhere in real life! They pop up in architecture, like the famous Louvre Pyramid in Paris, or even in the design of modern roofs. Knowing how to calculate their surface area can be super helpful in various fields, from engineering to crafting your own geometric art!
