Friday

August 22, 2014

August 22, 2014

Posted by **natalie** on Wednesday, April 4, 2007 at 9:00am.

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

**Related Questions**

geometry - 1.what is the area of a sector with a central angle of 160 degrees ...

trig - In a regular octagon, AB is a diagonal and CD joins the midpoints of two ...

math - The first term of a an infinite sequence is an equilateral triangle ...

math - A square whose side is 2m has it's corner cut away so as to form a ...

math - Find the area of the regular polygon. Round your answer to the nearest ...

geometry - find the area of a regular hexagon with the side length 4m. round to ...

Geometry - Find the area of a regular hexagon with side length of 10 centimeters...

Math/Geometry - Can you help me with this? Find the area of each regular polygon...

geomerty - Find the area of the regular polygon. Round your answer to the ...

Geometry - Please Help Me! Find the area of this polygon rround to the nearest ...