You have the following information about a prism:
Surface area = 56
Perimeter = 15
height = 3
In order to determine the base of the prism, take into account that the formula for the surface area of a prism is:
A = Ph + 2B
where P is the perimeter, A the surface area, h is the height and B is the area of the base.
Solve the previous equation for B:
A = Ph + 2B subtract Ph both sides
A - Ph = 2B divide by 2 both sides
(A - Ph)/2 = B
B = (A - Ph)/2
Replace the values of the parameters in the previous formula:
B = (56 - (15)(3))/2
B = (56 - 45)/2
B = 11/2 = 5.5
Hence, the area of the base of the prism is B = 5.5
