Question

if a polygon has an area of 7 cm² and is dilated by a factor of 3, what will be the area of the dilated polygon? area = _______ cm²

Explanation:

Step1: Recall the area - dilation formula

When a polygon is dilated by a scale factor \(k\), the ratio of the area of the dilated polygon \(A_{new}\) to the area of the original polygon \(A_{old}\) is \(k^{2}\). The formula is \(A_{new}=k^{2}\times A_{old}\).

Step2: Substitute the given values

Here, \(k = 3\) and \(A_{old}=7\mathrm{cm}^{2}\). Substitute these values into the formula: \(A_{new}=3^{2}\times7\).
First, calculate \(3^{2}=9\). Then, \(A_{new}=9\times7\).

Step3: Calculate the final area

\(9\times7 = 63\).

Answer:

\(63\)