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: Find square side length

The perimeter $P$ of a square is $P=4s$, where $s$ is side length. Rearrange to solve for $s$:
$s=\frac{P}{4}=\frac{20}{4}=5$ cm

Step2: Calculate square area

Area $A$ of a square is $A=s^2$. Substitute $s=5$:
$A=5^2=25$ cm²
(Alternatively, use the formula for area of a regular polygon: $A=\frac{1}{2}\times \text{apothem} \times \text{perimeter}=\frac{1}{2}\times2.5\times20=25$ cm²)

Answer:

25 cm²