Find the area of a regular octagon inscribed in a circle of radius 10cm.?

Question

Drawings, images

images, drawings

Answer 1

split the circle into 8 isosceles triangles, with the two equal sides corresponding to the radius of the circle (10cm).

a circle has 360° so dividing by 8 you get 45° for the apex angle of each isosceles triangle.

now with the use of trig, you can find an expression for the height of the triangle - 10sin45º.

the area of one triangle is given by the formula 1/2bh

where a = 10 b =10sin45º = 10*√2/2

so subbing these into the formula, you find that one triangle has area A = ½(10)(10*√2/2) = 25√2.

there are 8 triangles, so 1 octagon has area 8 x 25√2 = 200√2 cm²

= 282. 84 cm² -->final answer.

Answer 2

An octagon consists of 8 isosceles triangles, each having a central angle of 360/8 = 45°
The area will be 8(10sin(22.5))(10cos(22.5) = 800sin(22.5)cos(22.5) = 282.84 cm^2

Answer 3

http://mathforum.org/library/drmath/view/55034.html

there is an image there, might help