A prism measuring 5 ft tall with a triangular base whose sides measures 7 ft, 3 ft, and 9 ft. In the base, the distance from the 9 ft side to the opposite vertex is 2 ft.
so, what is it you want to know? Just FWIW, I doubt that the altitude as given is correct.
To find the volume of the prism, we need to multiply the area of the base by the height of the prism.
First, let's determine the area of the triangular base. We can use Heron's formula to find the area of a triangle given the lengths of its sides. Heron's formula states:
Area = √(s(s-a)(s-b)(s-c))
where 'a', 'b', and 'c' are the lengths of the sides of the triangle, and 's' is the semi-perimeter of the triangle.
In this case, 'a' is 7 ft, 'b' is 3 ft, and 'c' is 9 ft. We can calculate 's' as follows:
s = (a + b + c) / 2
s = (7 + 3 + 9) / 2
= 19 / 2
= 9.5 ft
Now we can use Heron's formula to find the area of the base:
Area = √(9.5(9.5-7)(9.5-3)(9.5-9))
Simplifying further:
Area = √(9.5 * 2.5 * 6.5 * 0.5)
= √(81.875)
≈ 9.05 ft^2 (rounded to two decimal places)
Next, we need to find the height of the prism, which is given as 5 ft.
Finally, we can calculate the volume of the prism by multiplying the area of the base by the height:
Volume = Base Area * Height
= 9.05 ft^2 * 5 ft
≈ 45.25 ft^3 (rounded to two decimal places)
Therefore, the volume of the prism is approximately 45.25 cubic feet.