The base of a right prism is a rhombus whose sides are 12 inch and whose longer diagonal is 15 inch. Find its volume.

volume = base x height

area of base:
construct a right angled triangle by drawing an altiude to the longer diagonal.
x^2 + 36 = 144
x = √108
there are 4 congruent right-angled triangles
area of base = 4((1/2)(6)(√108)
= 12√108

volume = 12√108 h
once you find out what the h is, you didn't state it, you can surely finish it.

The base of a right prism is a rhombus whose sides are 12 inch and whose longer diagonal is 12 inch. the height is 15

Find its volume.

The base of a right prism is a rhombus whose sides are 10 inch and whose longer diagonal is 12 inch. the height is 15

Find its volume.

To find the volume of a right prism, we need to know the area of the base and the height of the prism. In this case, the base of the prism is a rhombus.

To find the area of a rhombus, we can use the formula:

Area = (diagonal1 * diagonal2) / 2

The longer diagonal of the rhombus is given as 15 inches. However, we need to find the length of the shorter diagonal.

To find the length of the shorter diagonal, we can use the formula:

Shorter diagonal = 2 * (side^2) - (longer diagonal^2) / (2 * side)

Now, let's calculate the length of the shorter diagonal.

Shorter diagonal = 2 * (12^2) - (15^2) / (2 * 12) = 17 inches

Now that we have the length of both diagonals, we can calculate the area of the base:

Area = (15 * 17) / 2 = 127.5 square inches

Next, we need to find the height of the prism. Unfortunately, the height is not given in this question. If the height is given, we can simply multiply the area of the base by the height to find the volume.

For example, if the height is 10 inches, the volume of the prism would be:

Volume = 127.5 * 10 = 1275 cubic inches

Therefore, we cannot find the exact volume of the prism without knowing the height.