What is the area of a triangular prism with a base of 10 meters, height of 5 meters, and length of 15 meters?
A - 250 meters^2
B - 500 meters^2
C - 750 meters^2
D - 1000 meters^2
To find the area of a triangular prism, we need to calculate the combined area of all the faces.
First, let's find the area of the triangular base. The formula for the area of a triangle is (base * height) / 2.
In this case, the base of the triangle is given as 10 meters, and the height is given as 5 meters. Therefore, the area of the triangular base is (10 * 5) / 2 = 25 meters^2.
Now, let's find the area of the two rectangular faces of the prism. The formula for the area of a rectangle is length * width.
In this case, the length is given as 15 meters, and the width is equal to the base of the triangular face, which is 10 meters. Therefore, the area of each rectangular face is 15 * 10 = 150 meters^2.
Finally, to get the total area of the triangular prism, we add up the areas of all the faces: 25 meters^2 (triangular face) + 150 meters^2 (rectangular face) + 150 meters^2 (rectangular face) = 325 meters^2.
However, none of the given answer choices match this result. Therefore, it seems there might be a mistake in the options provided.
To find the area of a triangular prism, you'll need to calculate the area of the two triangular bases and the area of the three rectangular faces.
1. Calculate the area of one triangular base:
- The formula for the area of a triangle is 1/2 * base * height.
- The base of the triangular base is 10 meters, and the height is 5 meters.
- Therefore, the area of one triangular base is 1/2 * 10 * 5 = 25 square meters.
2. Calculate the area of the other triangular base:
- Since the triangular prism has two identical triangular bases, the area of the other base is also 25 square meters.
3. Calculate the area of the three rectangular faces:
- The formula for the area of a rectangle is length * width.
- In this case, the length is 15 meters, and the width is 10 meters (which is the base of the triangular base).
- Therefore, the area of each rectangular face is 15 * 10 = 150 square meters.
- Since there are three rectangular faces, the total area of the three faces is 3 * 150 = 450 square meters.
4. Calculate the total surface area of the triangular prism:
- The total surface area is the sum of the areas of the two triangular bases and the three rectangular faces.
- Total surface area = 2 * area of one triangular base + area of three rectangular faces
- Total surface area = 2 * 25 + 450 = 50 + 450 = 500 square meters.
Therefore, the area of the given triangular prism is 500 square meters.
So, the correct answer is B - 500 meters^2.