Remember that s represents the side length of a polygon.
See solution.
Practice makes perfect
We want to find the area of a regular hexagon given the apothem and the distance between the vertex and the center of a figure. Let's take a look at the given figure.
If we call the side length of the hexagon s, then the shorter leg of the drawn right triangle is 12 s.
Now, using the Pythagorean Theorem we can write the equation. According to this theorem the sum of the squared legs of a right triangle is equal to the squared hypotenuse.
13^2+(1/2 s)^2= 15^2
Let's solve the above equation. Notice that since s represents the side length, we will consider only the positive case when taking a square root of s^2.
The side length is approximately 15, not 7.5. Next, let's recall the formula for the area of a regular polygon.
A=1/2ans
In this formula a is the apothem, n is the number of sides, and s is the side length of a regular polygon. To evaluate the area of the given figure let's substitute 13 for a, 6 for n, and 15 for s.
