You can put this solution on YOUR website! Ok the perimeter is 48 inches. It is a regular hexagon (six sides) so this must mean each of the sides is equal in length. So 48/6 = 8 inches per side.
We know from the formula (where n is the number of sides) that each interior angle must equal 120 degrees.
Best thing here is to draw a hexagon. If you would like to see the one I drew, respond back so I email it to you. It will look like a square with two triangle on each end.
Now if we take say the left side of the hexagon, with the triangle shape, we know that the angle must be 120 degrees. If we draw a line from the left hand point down to the bottom we form a triangle.
We know that the angle top angle must be (120-90) = 30 degrees. So to find the base of length of the triangle we can use the Sine rule which is
If we half this number we get one side of a right angled triangle with the hypotenuse being 8 inches. The third side can be obtained using
So .
So we have a little right angled triangle with sides 4, sqrt48, and 8. The area of this triangle is given by 1/2 base times the height.
So we have the area of one of the small triangles. So the four triangles equals .
The remaining area is the square in the hexagon which is simply inches^2 (to 3 decimal places).
This is the long method, but there is a simple formula which is
where L equals the length of one of the sides of a regular hexagon.
It will make loads more sense with a diagram! Trust me! :-)
