The triangle on the left is a 5 - 12 - 13 right triangle
The area = (1/2) product of the legs = (1/2)(5)(12) = 30 units^2
Draw a perpendicular from C to DK.....call the intersection point E
So....in the middle....we have a rectangle with a width of 15 and a height of 12
So....the area = 15 * 12 = 180 units^2
And triangle CEK is a right triangle with CE = 12 and CK = 20
So...
EK = sqrt [ CK^2 - CE^2 ] = sqrt [ 20^2 - 12^2] = sqrt [ 400 - 144] = sqrt [ 256] = 16
So....the area of CEK = (1/2)(16)(12) = 96 units^2
So....the area of the trapezoid =
30 + 180 + 96 =
306 units^2
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