Use the image to answer the question.

Question

Create an illustration of a geometric shaped diagram. There's a triangle with sides measuring 16 meters, 14 meters, and 8 meters. From one side that measures 16 meters, a dashed perpendicular line leading to the vertex opposite of it is present, which measures 7 meters. Clearly indicate a right angle to the left of this perpendicular line. Then, create additional imagery of a prism and pyramid which both share a similar triangular base to the mentioned triangle and have heights of 15 meters each.

Use the image to answer the question.

An illustration shows a triangle with sides measuring 16 meters, 14 meters, and 8 meters. A dashed perpendicular line, from the side measuring 16 meters to the opposite angle, measures 7 meters. A right angle symbol is shown to the left of the perpendicular line.

A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape?

(1 point)
The volume of the prism is
m3.
The volume of the pyramid is
m3.
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Answer 1

both wrong

Answer 2

The volume of the prism is 480 m^3.

The volume of the pyramid is 160 m^3.

Answer 3

Let's start by finding the area of the base triangle. To do this, we can use Heron's formula since we know all three side lengths:

First, calculate the semi-perimeter:
s = (a + b + c) / 2
s = (16 + 14 + 8) / 2
s = 19

Now, calculate the area of the triangle using Heron's formula:
Area = sqrt[s * (s - a) * (s - b) * (s - c)]
Area = sqrt[19 * (19 - 16) * (19 - 14) * (19 - 8)]
Area = sqrt[19 * 3 * 5 * 11]
Area = sqrt[3135]
Area ≈ 56.03 m^2

Since the base triangle of the prism and pyramid have the same area, we can proceed to calculate their volumes:

Volume of the prism = base area * height = 56.03 * 15 = 840.45 m^3
Volume of the pyramid = (1/3) * base area * height = (1/3) * 56.03 * 15 = 280.15 m^3

Therefore, the volume of the prism is 840.45 m^3 and the volume of the pyramid is 280.15 m^3.