In triangle ABC, AB = 17, AC = 8, and BC = 16. Let D be the foot of the altitude from C to AB. Find the area of triangle ACD.
+129850 C
8 16
A D B
17
Using Heron's Formula.....the semi-perimeter = ( 17 + 8 + 16) / 2 = 41/2 = 20.5
And the area = sqrt [ ( 20.5 ( 20.5 -17) (20.5 - 16) (20.5 - 8) ] =
sqrt [ 20.5 * 3.5 * 4.5 * 12.5 ] =
sqrt [4035.9375 ]
And the area = (1/2) AB * CD
sqrt [ 4035.3975 ] = (1/2) (17) CD
sqrt [ 4035.3975] = 8.5 CD
sqrt [ 4035.3975 ] / 8.5 = CD ≈ 7.474
Area of triangle ACD = (1/2) CD * AD = (1/2) (7.474) * sqrt [ 8^2 - 7.474^2 ] ≈ 10.6615 units^2
