Three rectangular prisms have combined volume of 518 cubic feet prism a has one third the volume of prism b and prisms b and c have equal volume what is the volume of each prism

Translating the given problem into equation form:

Let A = volume of prism A

B = volume of prism B

C = volume of prism C

Eqn 1: A + B+ C = 518

Eqn 2: A = (1/3)B

Eqn 3: B = C

There are 3 equations and 3 unknowns, the system of linear can be solved. Using a calculator (preferably Casio 991-ES), yields:

A = 74 cu.ft

B = 222 cu.ft

C = 222 cu.ft

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!

e) none of the above because the measure of angle cba is 101°