Question

What is the surface area of the triangular prism?

(1 point)
 square centimeters

In the shape I can’t give exact details only numbers. The numbers are: 10, 8, 6, 9

Just use what you have and give me an answer pls

Answer 1

To calculate the surface area of a triangular prism, we need to know the area of the triangular base and the area of the three rectangular faces.

Let's assume:
- Base (b) of the triangle = 8 cm
- Height (h) of the triangle = 6 cm
- Length (l) of the prism = 10 cm

1. **Area of the triangular base**:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 6 = 24 \, \text{cm}^2
\]
Since there are two triangular bases, the total area for the triangular bases is:
\[
\text{Total Area}_{\text{triangles}} = 2 \times 24 = 48 \, \text{cm}^2
\]

2. **Area of the rectangular faces**:
- The first rectangle (base * length):
\[
\text{Area}_{\text{rect1}} = 8 \times 10 = 80 \, \text{cm}^2
\]
- The second rectangle (height * length):
\[
\text{Area}_{\text{rect2}} = 6 \times 10 = 60 \, \text{cm}^2
\]
- The third rectangle involves the side of the triangle. To find the side of the triangle (assuming it is a right triangle), we can calculate the hypotenuse (c):
\[
c = \sqrt{(8^2 + 6^2)} = \sqrt{(64 + 36)} = \sqrt{100} = 10 \, \text{cm}
\]
Then,
\[
\text{Area}_{\text{rect3}} = 10 \times 10 = 100 \, \text{cm}^2
\]

3. **Total surface area**:
\[
\text{Total Surface Area} = \text{Total Area}_{\text{triangles}} + \text{Area}_{\text{rect1}} + \text{Area}_{\text{rect2}} + \text{Area}_{\text{rect3}}
\]
\[
\text{Total Surface Area} = 48 + 80 + 60 + 100 = 288 \, \text{cm}^2
\]

Therefore, the surface area of the triangular prism is **288 square centimeters**.