~11.31
Pythagorean Theorem because it is a right triangle.
Set up a proportion
EA / EB = ED/ EC
16 / (5x + 2 + 16) = 12 / (12 + 24)
16/(5x + 18) = 12 / 36 Cross multiply
16 * 36 = (4x + 18)*12 Remove the brackets
576 = 48x + 216 Subtract 216 from both sides.
360 = 48x Divide by 48
360/48 = x
7.5 = x
from the question, (-2,2) and (1,2) have the same y value so you can use that as your base and easily find the perpendicular height using the y axis since it's parallel to the x axis.
the third point, (0,-6), to the base is your height
use the sum of the positive of the y values to find your height (because height can't be negative): 6+2 = 8
area of a triangle = 1/2 bh = 1/2 x 3 x 8 = 12
Note: 1/2 bh only works because (-2,2) and (1,2) form a line parallel to the x axis
I wish I could post a link to Wkipedia because I found a good explanation of corresponding angles.
7 and 3 are corresponding angles.