The base of a right prism is a rhombus with diagonals of 6 and 8. if the altitude of the prism is 12, what is the total surface area of this prism?

Check the picture below.

let's recall that a rhombus diagonals intersect at right-angles and that in a rhombus, slanted as it may be, the sides are all equal.

so we can find the area of one the triangles in the rhombus by simply using a base of 3 and a height of 4, and since there are four of those triangles, 4 times that much is the area of one of the rhombic faces.

as  you see in the picture, if we use the pythagorean theorem, we end up with a hypotenuse of 5, which is the length of the base sides on this prism, which also has four rectangular faces standing up vertically, each face is a 5x12 rectangle.

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi