63.0k views
4 votes
Write a formula for the area of the regular polygon. Solve the formula for the height h.

Write a formula for the area of the regular polygon. Solve the formula for the height-example-1

1 Answer

4 votes

Solution:

Part A:

The image of the regular polygon given is an octagon.

An octagon is a polygon with 8 sides.

To calculate the area of a regular polygon, the polygon is split into triangles and the area of triangles is summed up to get the area of the polygon.


\begin{gathered} \text{Area of triangle is given by}; \\ A=(1)/(2)bh \\ \text{where b is the base} \\ h\text{ is the height.} \\ \\ A\text{ polygon has n-triangles.} \\ \text{Therefore, the area of a regular polygon is;} \\ A=n*(1)/(2)bh \\ A=(n)/(2)bh \\ \\ \text{Also, the perimeter of the polygon is the sum of the outer sides, i.e, the sum of the base.} \\ P=n* b \\ A=(Ph)/(2) \\ \text{For an octagon, n = 8sides} \\ P=8b \\ \\ \text{Thus,} \\ A=(8bh)/(2) \end{gathered}

Therefore, the area of the regular polygon (octagon) is;


A=(8bh)/(2)

Part B:

To solve for the formula for the height h, we make h the subject of the formula;


\begin{gathered} A=(8bh)/(2) \\ \text{Cross multiplying:} \\ 2A=8bh \\ \text{Dividing both sides by 8b;} \\ h=(2A)/(8b) \end{gathered}

Therefore, the height is;


h=(2A)/(8b)

User Yunyi Hu
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories