The four sequential sides of a quadrilateral have lengths:

Question

a=3.6

b=5.1

c=8.5

d=10.2

The angle between the two smallest sides is <=108

What is the area of the figure?

Answer 1

we can get the area of the triangles using 1/2ab sin C = 1/2*3.6*5.1*sin(108°) = 8.73069881958951

By having a and b and the angle between them, we can get the diagonal length via the cosine law and we can use these sides to find the area of the other triangle.

Let's label the length of this diagonal x.

Then, x = √(a² + b² - 2ab cos X) = √(3.6² + 5.1² - 2*3.6*5.1 cos 108°) = 7.09345501384537

Then, we can get the area of the second triangle either by solving for one of the angles using the cosine law and using 1/2 ab sin C or use Abel's law.

Let's use Abel's law for variety.

p=(8,5 + 10.2+ 7.09345501384537)/2

A =√((p(p-a)(p-b)p-c) = 29.7892487755653

8.73069881958951 + 29.7892487755653 = 38.5199475951548