In a rectangular prism no width is given but there is a numbers in the top rectangle of 54 inches^2 the center rectangle is 36 inches^2 and the small rectangle to the side is 24 inches^2. How can you find the surface area

Answer 1

To find the surface area of the rectangular prism, we need to add up the areas of all six faces.

Let's denote the length of the rectangular prism as L, the width as W, and the height as H. From the given information, we can see that the area of the top face is LW = 54 inches^2, the area of the front face is WH = 36 inches^2, and the area of the side face is LH = 24 inches^2.

Now, we can set up a system of equations to solve for the dimensions of the rectangular prism:

LW = 54
WH = 36
LH = 24

From the first equation, we can solve for W:
W = 54/L

Substitute this into the second equation:
H(54/L) = 36
H = 36L/54
H = 2L/3

Now substitute both W and H into the third equation:
L(2L/3) = 24
2L^2/3 = 24
2L^2 = 72
L^2 = 36
L = 6 inches

Now we can find W and H:
W = 54/6 = 9 inches
H = 2(6)/3 = 4 inches

The surface area of the rectangular prism is:
2(LW + WH + LH)
2(6*9 + 9*4 + 6*4)
2(54 + 36 + 24)
2(114)
228 inches^2

So, the surface area of the rectangular prism is 228 square inches.