Question
Find the TOTAL surface area of this triangular prism in cm?
*Hint: Remember, the triangle is always the true base (bottom).
Answers:
24 cm2
192 cm2
202 cm 2
216 cm 2
*Hint: Remember, the triangle is always the true base (bottom).
Answers:
24 cm2
192 cm2
202 cm 2
216 cm 2
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the total surface area of a triangular prism, you need to calculate the area of the two triangular bases and the three rectangular sides. The formula for the total surface area \( SA \) of a triangular prism is:
\[
SA = 2 \times \text{Area of the triangle} + \text{Lateral Area}
\]
Where:
- The lateral area is the sum of the areas of the three rectangular faces.
Let's break down the components:
1. **Area of the triangular base** (\( A_{triangle} \)):
- If we know the base and height of the triangle, the area can be calculated using the formula:
\[
A_{triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
2. **Lateral Surface Area**:
- If the prism has a height (length) \( h \), and each side of the triangle has lengths \( a, b, \) and \( c \), the lateral surface area is the sum of the areas of the three rectangles:
\[
A_{lateral} = a \times h + b \times h + c \times h = h(a + b + c)
\]
3. **Total Surface Area**:
\[
SA = 2A_{triangle} + A_{lateral}
\]
For your question, if there are specific values for the dimensions of the triangle and the height of the prism, please provide those, and I can help you calculate the total surface area. Without those specific dimensions, we cannot determine the exact surface area solely from the options you provided.
\[
SA = 2 \times \text{Area of the triangle} + \text{Lateral Area}
\]
Where:
- The lateral area is the sum of the areas of the three rectangular faces.
Let's break down the components:
1. **Area of the triangular base** (\( A_{triangle} \)):
- If we know the base and height of the triangle, the area can be calculated using the formula:
\[
A_{triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
2. **Lateral Surface Area**:
- If the prism has a height (length) \( h \), and each side of the triangle has lengths \( a, b, \) and \( c \), the lateral surface area is the sum of the areas of the three rectangles:
\[
A_{lateral} = a \times h + b \times h + c \times h = h(a + b + c)
\]
3. **Total Surface Area**:
\[
SA = 2A_{triangle} + A_{lateral}
\]
For your question, if there are specific values for the dimensions of the triangle and the height of the prism, please provide those, and I can help you calculate the total surface area. Without those specific dimensions, we cannot determine the exact surface area solely from the options you provided.
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