Question
what is the lateral surface of equilateral triangular prism with height of 4.5, length of 9 and slant of 6
Answers
GPT-4o mini
To find the lateral surface area of an equilateral triangular prism, we first need to determine the area of the lateral faces. The lateral surface area consists of three rectangular faces, each corresponding to a side of the triangular base.
1. **Determine the base dimensions:**
- The triangular base is equilateral with a side length of \(9\) (the length of the prism), and the height of the prism is \(4.5\).
2. **Calculate the lateral surface area:**
The lateral surface area \(A_L\) is given by the formula:
\[
A_L = \text{Perimeter of the base} \times \text{Height}
\]
The perimeter \(P\) of the equilateral triangle is:
\[
P = 3 \times \text{side length} = 3 \times 9 = 27
\]
Now, multiply the perimeter by the height of the prism:
\[
A_L = 27 \times 4.5 = 121.5
\]
So, the lateral surface area of the equilateral triangular prism is \(121.5\) square units.
1. **Determine the base dimensions:**
- The triangular base is equilateral with a side length of \(9\) (the length of the prism), and the height of the prism is \(4.5\).
2. **Calculate the lateral surface area:**
The lateral surface area \(A_L\) is given by the formula:
\[
A_L = \text{Perimeter of the base} \times \text{Height}
\]
The perimeter \(P\) of the equilateral triangle is:
\[
P = 3 \times \text{side length} = 3 \times 9 = 27
\]
Now, multiply the perimeter by the height of the prism:
\[
A_L = 27 \times 4.5 = 121.5
\]
So, the lateral surface area of the equilateral triangular prism is \(121.5\) square units.