Question

I need help with this question

1) Find the area of a regular hexagon with the given measurement.

48-inch perimeter

A = sq. in.

A =

Answer 1

You need to write one question per post.
I'll help you with the first one here.

Answer 2

The perimeter is 48 inches.
What is the length of each side?

Answer 3

Uh, 8?

Answer 4

Yes.
Now we can divided the hexagon into 6 congruent triangles.

Answer 5

The area of the hexagon is 6 times the area of each triangle.
What do you need to know to be able to find the are of a triangle?

Answer 6

The length of each side?

Answer 7

There is a way to find the area that way, but the more common way is to know the base and the height.

Answer 8

Let's look at the hexagon.
The point inside where all the triangles meet is the vertex of 6 congruent angles.
Altogether, the 6 angles go around a full circle, so altogether they measure 360 degrees.
Each angle measures 360 deg/6 = 60 deg.

Answer 9

Also, a polygon of n sides has the sum of the measures of the interior angles

180(n - 2)

For our hexagon, with 6 sides, n = 6, so

180(6 - 2) = 180(4) = 720

The sum of the measures of the interior angles is 720 deg.
That means each interior angle is 120 deg.