This is the concept of numbers, given that the G.C.D two numbers (a,b)=6 and the L.C.M (a,b)=180, to find the possible number we do as follows;
L.C.M =a*b=180
since 6 is a multiple of a and b, then the numbers could be:
180/6
=30
hence these numbers could be (6,30)
Number of different bases for each one:
1 1 12 --->1 1 12, 1 12, 1 ----- 2 of them
1 2 6 ---> 1 2 6, 1 6, 2, 2 6 1 --- 3 of them
1 3 4 ---> 1 3 4, 1 4 3, 3 4 1 --- 3 of them
2 2 3 ---> 2 2 3, 2 3 2 ----- 2 of them
Answer-10 different prisms
check the picture below.
you can check in your calculator, make sure your calculator is in Degree mode.
(a+b)(a-b) = a^2 - b^2
(1+5/6) (1-5/6) = 1^2 - (5/6)^2 = 1 - 25/36 = 36/36 - 25/36 = (36-25)/36 = 11/36
11/36 is your answer
