Question

Write a formula for the area of the regular polygon. Solve the formula for the height h. Whoever answer gets brainliest pls help

Answer 1

PROBLEM STATEMENT

Given the regular polygons, we are asked to find their area and hence solve for height H.

SOLUTION

The definition of the area of a polygon is the measure of the area that is enclosed by it. As polygons are closed plane shapes, thus, the area of a polygon is the space that is occupied by it in a two-dimensional plane.

To find the area of a regular polygon, we would have to split the polygons into triangles. We must note the following;

a) The first polygon is a pentagon therefore, it would have five sides and five possible triangles.

b) The second polygon is also an octagon, with 8 sides and 8 possible triangles.

We should also note that the area of a triangle is given as;

$\text{Area of triangle=}\frac{1}{2}\times\text{base x height}=\frac{1}{2}bh$

We can imply that;

$\begin{gathered} \text{Area of pentagon=5 x Area of a triangle}=\frac{5}{2}bh \\ \text{Area of octagon=8 x Area of a triangle}=\frac{8}{2}bh \end{gathered}$

Since the number of sides can change depending on the type of polygon, the area of the polygon would be;

Answer 1:

$\text{Area of regular polygon =}\frac{n}{2}\times bh$

We can then derive the height by making h the subject of formula in the expression above;

$\begin{gathered} A=\frac{n}{2}\times bh \\ \text{Cross multiply} \\ \text{nbh}=2A \\ Divide\text{ both sides by nb} \\ \frac{\text{nbh}}{nb}=\frac{2A}{nb} \\ h=\frac{2A}{nb} \end{gathered}$

Answer 2:

$h=\frac{2A}{nb}$