Answer:
A = 12cm^2
? = 2cm
Step-by-step explanation:
1) First, I color-coded your image to represent the equal side lengths (red = 8, blue = 6). You can determine this by looking at where the lines end (e.g. for the given 8cm lines they end at the same points as the unknown verticle lines, apply this theory to the horizontal 6cm lines as well).
2) Subtract all of the given areas from the surface area to get the total amount of area that we are missing:
152 - 48 - 16 - 48 - 16 = 24cm^2
3) Divide 24 by 2 (which is 12) to get A, we know that the area of the top and bottom A will be equal since they will both have the same length and width (6cm and the value of ? in cm)
4) We know that the equation for the Area of a square is: L * W = A cm^2
So let's plug in our known values: L = ?, W = 6cm, A = 12cm^2
L * 6 = 12
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6 <---- Divide both sides by 6 to get 2 as the length
L = 2
Therefore, 2cm is our missing '?' value, since it is the equivalent variable for our length.
I hope this helps!
