Answer:
d
Step-by-step explanation:
this shape is made up of a triangular prism and a rectangular prism. the formula for the volume of a prism (any prism, doesn't matter) is base area times height. the base areas of the rectangular prism can be found by multiplying 4*12, as these are the dimensions of the base rectangle. 4*12=48. we now multiply this number by the height of the rectangular prism as shown in the volume of a prism formula. the height of the rectangular prism is 14, so 48*14=672. the volume of the rectangular prism is 672 cm^3.
now for the triangular prism. the bases of the triangular prism are the two triangle shapes on the ends; a prism is named after the shape of its base, so be sure to note that you use the triangles for the formula and not the rectangle on the bottom. to find the area of one of these bases (they are both the same), we use the triangle area formula, 1/2*base*height. the base of the triangle shape is 4 units long, as seen by the measurements of the rectangle this triangle sits on top of. to find the height of this triangle, which isn't given, we must use the pythagorean theorem, a^2+b^2=c^2. c in this case is equal to 4 as that is the hypotenuse, and a and b are interchangeable. since the pythagorean theorem only works for right triangles, we must cut the base length in half to assume that the final side is a vertical line, which will give us the height of the original triangle. (note: halving the base length in order to apply the pythagorean theorem only works in this case because both of the other sides are equal length, as we can see on the far triangle, so make sure this applies before trying it in another context) the halved base length is 2, and this number can be either a or b, doesn't matter because the formula adds them. so: (2)^2+b^2=4^2. 2^2 is 4, and 4^2 is 16. 4+b^2=16. subtract 4 from both sides, leaving you with b^2=12, and to get rid of the square on b you take the square root of both sides. so the height of this triangle is the square root of 12, which doesn't need to be simplified if you have a calculator that can process square root input. so to find the area of this triangle, we convert the equation 1/2*base*height into 1/2*4*square root of 12. this gets you about 6.93. to find the total volume of this prism, you multiply the base area times height. as we just figured out, the base area is 6.93, and the height is 12, because this is the length between the two bases, which are the triangles. so, 6.93*12=83.16 is the volume of the triangular prism. the final step is to add this to the volume of the rectangular prism, which is 672. 672+83.16= 755.16 cm^3.
hope this helps! :)
