The base of a hexagonal prism has an area of 96 square inches. The height of the prism is 9 inches. Find the volume of the prism.

The volume of the prism is 864 inches^3.

Step-by-step explanation:

The basic formula for the volume of a prism is:

V = Ah

where:

V = Volume of prism

A = Area of uniform cross-section or base of prism = 96 inches^2

h = Perpendicular height of prism = 9 inches

Substitute the values given in the question into the formula.

V = 96 × 9

V = 864 inches^3

answer: 15

step-by-step explanation:

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!