Question

a hexagon has a radius measuring 23 cm. what is the approximate area of the hexagon?○ 686.6 square cm○ 793.5 square cm○ 1374.4 square cm○ 1587.0 square cm

Explanation:

Step1: Recall area formula for regular hexagon

The area $A$ of a regular hexagon with radius $r$ is $A = \frac{3\sqrt{3}}{2}r^2$

Step2: Substitute $r=23$ cm into formula

$A = \frac{3\sqrt{3}}{2} \times (23)^2$

Step3: Calculate $23^2$ first

$23^2 = 529$

Step4: Compute the constant and multiply

$\frac{3\sqrt{3}}{2} \approx \frac{3\times1.732}{2} = 2.598$
$A \approx 2.598 \times 529$

Step5: Final multiplication

$2.598 \times 529 \approx 1374.4$

Answer:

1374.4 square cm