Find the area of quadrilateral ABCD SolutionArea of triangle

Solution

Area of triangle ABD = (1/2)*65*130sin80 = 4160.81 ft^2

Applying cosine rule in triangle ABD to find BD:

BD^2 = 65^2 +130^2 -2*65*130*cos80 =18190.346

BD = 134.87 ft

Triangle BCD:

apply cosine rule : 134.87^2 = 120^2+ 120^2 -2*120*120cosC

cosC =0.368 ; C = 68.407 deg

Area of triangle = (1/2)*120*120*sin68.407 = 6694.714 ft^2

Are of quadilateral = Area of triangle ABD + Area of triangle BCD = 10855.52 ft^2

Option A