SAT Quadrilaterals

Correct Answer: C

Solution:

Tip: Area of a square with side length $s: A_{\square} = s^2.$
To find the area of the shaded region, we must subtract from the area of the big square the areas of the four small squares.

$\begin{array}{r c l} A_{\text{shaded}} &=& A_{\text{big}\ \square} - 4\cdot A_{\text{small}\ \square}\\ A_{\text{shaded}} &=& 8^2 - 4\cdot 1^2\\ A_{\text{shaded}} &=& 64 - 4\\ A_{\text{shaded}} &=& 60\\ \end{array}$

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Incorrect Choices:

(A)
If you use the formula for finding the perimeter of a square, $P_\square = 4s,$ instead of that for finding the area of a square, $A_{\square} = s^2,$ you will get this wrong answer.

(B)
If you find the sum of the perimeters of the big square and the four small squares, you will get this wrong answer.

(D)
If from the area of the big square you subtract the area of only one square, instead of the sum of the areas of all four small squares, you will get this wrong answer.

(E)
If you find the sum of the areas of the big square and the four small squares, you will get this wrong answer.