Polygon A has an area of 27r square meters. Polygon A is dilated by a scale factor of 3 to create Polygon B. What is the area in square meters of Polygon B?
A. 243r square meters
B. 9r square meters
C. 729r square meters
D. 81r square meters
The area of a shape after dilation is equal to the scale factor squared times the original area. In this case, the scale factor is 3, so the area of Polygon B is equal to $(3^2)(27r)=\boxed{\textbf{(C) }729r\text{ square meters}}$.
To find the area of Polygon B, we need to square the scale factor and multiply it by the area of Polygon A.
The scale factor is 3, so we square it to get 3^2 = 9.
The area of Polygon A is 27r square meters.
Now, we calculate the area of Polygon B by multiplying the scale factor squared (9) by the area of Polygon A (27r):
Area of Polygon B = 9 * 27r = 243r square meters.
Therefore, the area of Polygon B is 243r square meters, which corresponds to option A.