A regular triangular pyramid has an altitude of 15.0 m and the base is 8.00 m on a side. Find the area of a section made by a plane parallel to the base and 8.00 m from the vertex.

To find the area of the section made by a plane parallel to the base and 8.00 m from the vertex, we need to calculate the area of the section's base.

First, let's find the length of the side of the smaller triangle formed by the plane and the pyramid's base. This can be done using the concept of similar triangles.

Since the plane is parallel to the base, the smaller triangle formed is similar to the base triangle. Let's assume that the length of the side of the smaller triangle is x.

Now, we can set up the following proportion:

(x / 8.00) = (15.00 / 8.00)

Cross multiplying, we get:

8.00 * x = 15.00 * 8.00

x = (15.00 * 8.00) / 8.00

x = 15.00

Now we know that the length of the side of the smaller triangle is 15.00 m.

To find the area of the section's base, we can calculate the area of the smaller triangle. The formula for the area of a triangle is:

Area = (1/2) * base * height

In this case, the base of the smaller triangle is x = 15.00 m, and the height is 8.00 m.

Area = (1/2) * 15.00 * 8.00

Area = 60.00 m²

Therefore, the area of the section made by the plane parallel to the base and 8.00 m from the vertex is 60.00 m².