I2019m Regular N-Gon, The Sides Are 4.8cm In Length, The Apothem Is 7.4cm, And The Area Is 177.6cm^2, How Many Sides Are In The Polygon

I'm regular n-gon, the sides are 4.8cm in length, the apothem is 7.4cm, and the area is 177.6cm^2

How many sides are in the polygon

Answer: 10 Sides

First of all let us define the important terms for this problem.

A Polygon also known as a n-gon is a flat figure that has atleast three or more sides and angles.

A Regular Polygon is a type of polygon with all equal sides.

Attached below is an example of a regular polygon, namely a hexagon. Hexa means six, that means the polygon has six sides.

as shown in the image above, the Apothem is a line from the center of the polygon to the midpoint of one of the sides.

Step-by-step explanation:

Step 1:

First, take note that a regular polygon can be divided into equal triangles with the same number as its sides, as shown in the attached figure.

We then use the formula for the area of the triangle which is:

Area = $\frac{1}{2} (base)(height)$

Step 2:

using the formula of the triangle an area same with the image below:

note: in this case, the base for the formula is the side divided by 2 and the height is the apothem

Area = $\frac{1}{2} (\frac{4.8}{2})(7.4)$

Area = 8.88 cm2

Step 3:

We then multiply the area by 2 to get the area of the whole triangle that equates to one side of the polygon.

Area of one side = 8.88 x 2

Area of one side = 17.76 cm^2

Step 4:

Next, we divide the given total area (177.6 cm^2) by the Area of one triangular side to get the number of sides of the polygon.

Sides = $\frac{177.6}{17.76}$

Sides = 10

Answer = 10 sides

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