Question

in a triangular prism there are three rectangles with measurements of 19 x 10 and two triangles with measurements 8 x 6. What is the surface area of this prism?

Answer 1

To find the surface area of the triangular prism, we need to calculate the areas of the rectangular faces and the triangular bases.

1. **Calculate the area of the triangular bases:**
The area \( A \) of a triangle can be calculated using the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
For the triangle with a base of 8 and height of 6:
\[
A = \frac{1}{2} \times 8 \times 6 = \frac{1}{2} \times 48 = 24 \text{ square units}
\]
Since there are two triangular bases, the total area for the triangles is:
\[
\text{Total area of triangles} = 2 \times 24 = 48 \text{ square units}
\]

2. **Calculate the area of the rectangular faces:**
There are three rectangular faces, each with a dimension of 19 by 10. The area \( A \) of a rectangle is calculated with:
\[
A = \text{length} \times \text{width}
\]
Thus, the area of one rectangle is:
\[
A = 19 \times 10 = 190 \text{ square units}
\]
Since there are three rectangles, the total area for the rectangles is:
\[
\text{Total area of rectangles} = 3 \times 190 = 570 \text{ square units}
\]

3. **Calculate the total surface area of the prism:**
The total surface area \( SA \) is the sum of the total area of the triangular bases and the total area of the rectangular faces:
\[
SA = \text{Total area of triangles} + \text{Total area of rectangles}
\]
\[
SA = 48 + 570 = 618 \text{ square units}
\]

Thus, the surface area of the triangular prism is **618 square units**.