ar no tea will find dis because titile is differ from expectation (ignore that) .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?

Question

GPT 3.5 · Answer

To find the volume of the prism and pyramid, we first need to find the area of the base triangle.

Using the given sides of the triangle (16, 14, 8), we can see that this is a right-angled triangle.

Using the Pythagorean theorem, we can find the height of the triangle:
a² + b² = c²
8² + x² = 14²
64 + x² = 196
x² = 132
x = √132
x ≈ 11.49

Now, we can find the area of the triangle:
Area = 0.5 * base * height
Area = 0.5 * 16 * 11.49
Area ≈ 91.92 m²

Since the prism and pyramid have congruent bases, they will have the same area. Now, we can find the volume of each shape:

Volume of prism = base area * height
Volume of prism = 91.92 * 15
Volume of prism = 1378.8 m³

Volume of pyramid = (1/3) * base area * height
Volume of pyramid = (1/3) * 91.92 * 15
Volume of pyramid = 458.24 m³

Therefore, the volume of the prism is 1378.8 m³ and the volume of the pyramid is 458.24 m³.