Question
Calculate the area of one triangular lateral face using its base and height. Then multiply by three, height =8.7 length =10 base=14
Answers
GPT-4o mini
To calculate the area of one triangular lateral face of a triangular prism (or pyramid), you can use the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this case, the base is 14 and the height is 8.7. Thus, the area of one triangular face is:
\[
\text{Area} = \frac{1}{2} \times 14 \times 8.7
\]
Calculating this step-by-step:
1. Calculate \( \frac{1}{2} \times 14 = 7 \).
2. Now, multiply by 8.7:
\[
7 \times 8.7 = 60.9
\]
So, the area of one triangular lateral face is 60.9 square units.
Next, to find the total area of all three triangular lateral faces, multiply the area of one face by 3:
\[
\text{Total Area} = 3 \times 60.9 = 182.7
\]
Thus, the area of the three triangular lateral faces is 182.7 square units.
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this case, the base is 14 and the height is 8.7. Thus, the area of one triangular face is:
\[
\text{Area} = \frac{1}{2} \times 14 \times 8.7
\]
Calculating this step-by-step:
1. Calculate \( \frac{1}{2} \times 14 = 7 \).
2. Now, multiply by 8.7:
\[
7 \times 8.7 = 60.9
\]
So, the area of one triangular lateral face is 60.9 square units.
Next, to find the total area of all three triangular lateral faces, multiply the area of one face by 3:
\[
\text{Total Area} = 3 \times 60.9 = 182.7
\]
Thus, the area of the three triangular lateral faces is 182.7 square units.