Answer:
Explanation:
You cannot do this unless you are certain that P is the center of the octagon. I don't know if that's solvable from the information given. So I will make the assumption that P is the center.
Determine the midpoint of BC. Call it E. Draw a line from P to E. By symmetry EP = AP. BE = 1/2 * BC = 19/2 = 9.5 by construction
You have a trapezoid witch is 1/4 the area of the octagon. Three more trapezoids can fit into the octagon.
Formula
Area = (AP + BE)*PE / 2
Givens
AP = 12
BE = 9.5
PE = 12
Solution
Put the givens and constructions into the formula
Area = (12 + 9.5)*12/2
Area = 21.5 * 12/2
Area = 21.5 * 6
Area = 129
That's the area of one of the trapezoids. Multiply the area here by 4.
You get 516.