Question

a square has an apothem measuring 2.5 cm and a perimeter of 20 cm. what is the area of the square, rounded to the nearest square centimeter? 13 cm² 25 cm² 50 cm² 100 cm²

Explanation:

Step1: Recall the formula for the area of a regular polygon

The formula for the area of a regular polygon is \(A=\frac{1}{2}aP\), where \(a\) is the apothem and \(P\) is the perimeter.

Step2: Substitute the given values into the formula

Given \(a = 2.5\) cm and \(P=20\) cm.
Substitute into \(A=\frac{1}{2}\times a\times P\), we get \(A=\frac{1}{2}\times2.5\times20\).
First, calculate \(\frac{1}{2}\times20 = 10\).
Then, \(A=10\times2.5\).

Step3: Calculate the value of \(A\)

\(A = 25\) \(cm^{2}\)

Answer:

\(25\) \(cm^{2}\) (the second option)