SOLUTION: I need help in figuring out how to solve this problem. It is very confusing to me. I'd like to know how to work it out. Find the area of a regular octagon with side length 5cm

Algebra ->  Surface-area -> SOLUTION: I need help in figuring out how to solve this problem. It is very confusing to me. I'd like to know how to work it out. Find the area of a regular octagon with side length 5cm       Log On


   

Question 47531: I need help in figuring out how to solve this problem. It is very confusing to me. I'd like to know how to work it out.
Find the area of a regular octagon with side length 5cm and apothem 6cm.
Find the volume of a square pyramid with height 12cm and slant height 15cm.
Please help!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the area of a regular octagon with side length 5cm and apothem 6cm.
Connect the center to each of the vertices thus forming eight triangles.
The area of one of these triangles = (1/2)5*6= 15 cm^2
The area of the octagon = 8(15)=120 cm^2
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Find the volume of a square pyramid with height 12cm and slant height 15cm.
Draw a right triangle with slant height as the hypotenuse and height as
one of the sides. The base will be sqrt(15^2-12^2)= 9 cm
Then the diagonal of the base of the pyramid will be 18 cm
Find the side of the base of the pyramid as side^2 + side^2=18^2
2side^2=324
side= sqrt(162) and area of base= 162 cm^2
Then Volume= (1/3)Base*height
=(1/3)(162)12= 648 cm^3
Cheers,
Stan H.