The four sequential sides of a quadrilateral have lengths a = 4.9 , b = 5.3 , c = 7.6 , and d = 9.7 (all measured in yards). The angle between the two smallest sides is α = 117 ° .

Question

What is the area of this figure?

area =_________  yd²

Your answer should be accurate to 6 decimal places.

Answer 1

If angle A = 117° then area A₁ = 1/2·4.9·5.3sin117° = 11.56971972. By cosine theorem BC = 8.699440589.

Half perimeter of big triangle is s = 12.99972029. By Heron's formula area of big triangle A₂ = 31.56018581.

Total area of figure A₀ = A₁ + A₂ = 43.12990553 = 43.129906