Answer: Choice B, 8 square cm
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Explanation:
A1 = shaded area inside larger rectangle
A2 = shaded area inside smaller rectangle
A3 = unshaded overlapping region
A4 = A1+A2 represents the area of the entire 6 by 8 rectangle
A4 = 8*6
A4 = 48
Similarly,
A5 = A2+A3 is the area of the entire 4 by 5 rectangle
A5 = 4*5
A5 = 20
So we know that
A4 = A1+A3 = 48
A5 = A2+A3 = 20
Or in short,
A1+A3 = 48
A2+A3 = 20
Subtract the equations
A1+A3 = 48
A2+A3 = 20
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A1-A2 = 28
The total shaded region is 52, which means,
A1+A2 = 52
The new system of equations is
A1-A2 = 28
A1+A2 = 52
which combine to 2A1 = 80 and that solves to A1 = 40
If A1 = 40, then A2 = 12 after using A1+A2 = 52
Then we use A1+A3 = 48 to find that A3 = 8
