The apothem of a 40 -sided regular polygon is 11.7 cm . What is its area if each side measures 1.84 cm ?
Select one:
a.
b.
c.
d.

To find the area of a regular polygon, you can use the formula:

Area = (Perimeter × Apothem) / 2.

In this case, the perimeter of the polygon is the number of sides multiplied by the length of each side. For a 40-sided polygon with each side measuring 1.84 cm, the perimeter will be:

Perimeter = 40 × 1.84 cm = 73.6 cm.

Now, plug the values into the area formula:

Area = (73.6 cm × 11.7 cm) / 2 = 430.56 cm².

Since the closest option to this value is (b) , that would be your answer!

Now let’s sprinkle in some extra knowledge!

Polyhedrons have fascinated mathematicians for centuries. The study of regular polygons dates back to Ancient Greece, particularly with philosophers like Euclid, who explored the properties of shapes. The Greeks were particularly keen on understanding how these shapes interacted in a geometrical space, setting the foundation for modern geometry.

When applying the concept of area in real life, think about why it matters! Knowing the area of a space can help in tasks like laying down flooring, painting walls, or even farming land. Calculating accurately means that projects come out just right, saving time and resources – a win-win!