Question

which pair of squares have equivalent areas shaded? choose 1 answer:

Explanation:

Step1: Recall area formula for square

The area of a square is $A = s^2$, where $s$ is the side - length. For a right - triangle formed by the diagonal of a square, its area is $A=\frac{1}{2}s^2$.

Step2: Analyze option A

In the first square of option A, the shaded part is a right - triangle with area $\frac{1}{2}s^2$. In the second square of option A, the shaded part is a rectangle with area $\frac{1}{2}s^2$ (assuming the square is divided into two equal rectangles), where $s$ is the side - length of the original square.

Step3: Analyze option B

In the first square of option B, the shaded part is a right - triangle with area $\frac{1}{2}s^2$. In the second square of option B, the shaded part is a rectangle with area $\frac{1}{2}s\times s=\frac{1}{2}s^2$ if the side of the square is $s$, but the orientation and division are different from the first square's shaded part in a non - equivalent way in terms of shape and position within the square.

Step4: Analyze option C

The first square has a shaded right - triangle with area $\frac{1}{2}s^2$. The second square is a smaller square, and the shaded right - triangle within it has a different area as the side - length of the smaller square is different from the side - length of the first square.

Answer:

A. The first pair of squares have equivalent shaded areas.