SOLUTION: Determine the area of the regular octagon circumscribing a circle having an area of 126 m2. A. 127.83 m2 B. 132.90 m2 C. 119.05 m2 D. 113.44 m2

Question 1153292: Determine the area of the regular octagon circumscribing a circle having an area of 126 m2.
A. 127.83 m2
B. 132.90 m2
C. 119.05 m2
D. 113.44 m2
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Draw this
The area of the circle is 126 m^2=pi*r^2
therefore, r=6.333
Each of the 8 parts of the octagon is a triangle with central angle 45 deg
Draw a perpendicular to the side, and this bisects the central angle.
That triangle has angle 22.5, the opposite side is half the length of a side of the octagon, and the perpendicular line is the adjacent side.
cos22.5=adj/6.333; adj side =5.851
sin 22.5=opp/6.333, opp side=2.424
the side of the octagon is 4.848, double the above for sin 22.5
the altitude is 5.851
1/2 that product is the area of the triangle.
There are 8 such triangles, so 4 times the product is the answer or 113.46 m^2.
D.

RELATED QUESTIONS
A square having an area of 48 m2 is inscribed in a circle which is inscribed in a regular (answered by Edwin McCravy)

What is the area of the kite? 90 m2 108 m2 135 m2 216 m2 (answered by Fombitz)

5. Use formulas to find the lateral area and surface area of the given prism.... (answered by Alan3354)

A regular octagon has a side length of 8 m and an area of approximately 309 m2. The side... (answered by Alan3354)

What is the diameter of a circle that has an area of 36 pie... (answered by richard1234)

A swimming pool is constructed in the shape of two intersecting identical circles having... (answered by ikleyn)

A patio has an area of 90 m2. What is the area of the patio in... (answered by ewatrrr)

What's the area of an ellipse with the major axis 20 m and the minor axis 10 m? Round... (answered by Alan3354,fractalier)

Please help me, I don't understand how to do this at all- "The volumes of two similar... (answered by jorel1380,Alan3354)