Question

Please help me thank you.

Answer 1

The shape given is a triangular prism, since it has two triangular bases and three sides that are rectangles.

The equation for the volume of a triangular prism is V = A(l), where A = area of the triangular base and l = length of the prism/rectangular side.

We know that the triangular base is an equilateral triangle with side lengths of 10yd (outline in blue in picture). The equation for the area of an equilateral triangle is
`A = ( √(3) )/(4) s^(2)`, where s = the length of the side of the triangle.

Since we know s = 10 yds, plug that into the equation to find the area of the triangular base:

`A = ( √(3) )/(4) s^(2)\\ A = ( √(3) )/(4) (10)^(2)\\ A \approx 43.3\: yd^(2)`

The area of the triangular base, A, is about 43.3
`yd^(2)`. We also know that l, the length of the prism/rectangular side (outlined in green in the picture), is 29yd. Knowing A and l, we can plug these values into the equation for the volume of a triangular prism to get your answer:

`V = A(l)\\ V = (43.3 \: yd^(2))(29\:yd)\\ V = 1255.7 \ yd^(3)`

The volume of the given prism is B)
`1255.7 \ yd^(3)`.