Answer :
The length of the apothem of the pentagon is approximately 11 meters.
What is a polygon?
Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons etc.
Here, we have,
To solve this problem, we can use the formula for the area of a regular pentagon:
A = (5/2) × s × a
Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).
We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:
118.25 = (5/2) × 4.3 × a
Divide both sides by (5/2) x 4.3:
a = 118.25 / ((5/2) × 4.3)
= 118.25 / 10.75 ≈ 11 meters
Therefore, the length of the apothem of the pentagon is approximately 11 meters.
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Final answer:
To calculate the apothem of a regular pentagon given its area and side length, use the area formula of a regular polygon, leading to an apothem length of approximately 11 meters.
Explanation:
To find the length of the apothem of a regular pentagon with a given area and side length, we first recall the formula for the area of a regular polygon: Area = (Perimeter × Apothem)/2. In this case, we are given that the area of the pentagon is 118.25 square meters and each side measures 4.3 meters. Therefore, the perimeter of the pentagon is 5 × 4.3 meters.
Substituting the known values into the formula gives us:
- Area = (5 × 4.3 × Apothem)/2
- 118.25 = (21.5 × Apothem)/2
- 236.5 = 21.5 × Apothem
- Apothem = 236.5 / 21.5
Performing the division gives us the apothem length, which is approximately 11 meters.
