Pentagon ABCDE has a vertical line of symmetry. What is the y-coordinate of vertex C so that the area of the pentagon is 50 square units?
+129899 Note that if we connect BD we have square ABDE with a side = 4
So...its area = side^2 = 4^2 = 16
y coordinate of midpoint of BD = 4
Then the area of triangle BDC = 50 - 16 = 34
So....the area of this triangle = (1/2) base * height =
(1/2) (BD) (height) =
(1/2) (4) height = 34
2 * height = 34
height = 34/2 = 17
So.... C = (2, y midpoint of BC + 17 ) = (2, 4 + 17) = (2 , 21)
