# Math--Area

posted by
**natalie**
.

Find the area of each regular polygon to the nearest tenth. Octagon with side length of 10 kilometers.

Heres what I tried; but I don't know if im on the right track.

Area=1/2 * Perimeter* Apothem

Perimeter=base of octagon* number of sides

Perimeter=10*8=80 km.

SO A=40a

(1/2 of 80 times apothem)

How do I find the apothem of the octagon?

Work on one of the 8 triangles, since they are all equal

Such a triangle is isosceles with a 45º formed by the equal sides and the other side is 10 km.

the other two angles are 67.5º each.

The apothem, which is simply the perpendicular distance from the centre of your regular polygon to one of the sides. It becomes the height of the triangle

Let the height be h, and use trig.

tan 67.5 = x/5

x = 5 tan 67.5 = 12.071

so the area of one triangle = 1/2 * 10 * 12.071 = 60.355....

the area of the octogon is 8 times that