Question

surface area of triangular prism with height of 3, width of 4, slant of 5 and length of 11

Answer 1

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

1. **Area of the triangular base**:
The triangular base has a height (h) of 3 and a base (b) of 4. The area \( A \) of a triangle is given by the formula:
\[
A = \frac{1}{2} \times b \times h
\]
Substituting in the values:
\[
A = \frac{1}{2} \times 4 \times 3 = \frac{12}{2} = 6
\]
Therefore, the area of one triangular base is 6. Since there are two triangular bases, the total area for both bases is:
\[
2 \times 6 = 12
\]

2. **Area of the rectangular faces**:
There are three rectangular faces corresponding to each side of the triangular base:
- The first rectangle corresponds to the base of the triangle (4) and has a length of the prism (11):
\[
A_1 = \text{base} \times \text{length} = 4 \times 11 = 44
\]

- The second rectangle corresponds to the height of the triangle (3) and has a length of the prism (11):
\[
A_2 = \text{height} \times \text{length} = 3 \times 11 = 33
\]

- The third rectangle corresponds to the slant side of the triangle (5) and has a length of the prism (11):
\[
A_3 = \text{slant} \times \text{length} = 5 \times 11 = 55
\]

Adding these areas together:
\[
A_{rectangles} = A_1 + A_2 + A_3 = 44 + 33 + 55 = 132
\]

3. **Total surface area**:
The total surface area \( SA \) of the prism is the sum of the area of the triangular bases and the area of the rectangular faces:
\[
SA = A_{bases} + A_{rectangles} = 12 + 132 = 144
\]

Thus, the total surface area of the triangular prism is **144 square units**.