What is the area of the square below?
A square is shown with a dashed segment from a vertex to the center. The dashed segment is 12 centimeters.
(1 point)
Responses
16.97 cm²
16.97 cm²
72 cm²
72 cm²
144 cm²
144 cm²
288 cm²
To find the area of the square, we need to find the length of its sides. Since the dashed segment is from a vertex to the center, it is also a radius of the square. Therefore, the length of the diagonal (the dashed segment) is equal to twice the radius.
Since the dashed segment is 12 centimeters, the radius of the square is half of that, which is 6 centimeters.
The length of each side of the square is equal to the diameter, which is twice the radius. So the length of each side is 2 * 6 cm = 12 cm.
To find the area of a square, we square the length of one side. In this case, the area of the square is 12 cm * 12 cm = 144 cm².
Therefore, the correct answer is 144 cm².