Question 47531
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
=============================================
 
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.