Answer:
37.6 yd^2 to the nearest tenth.
Step-by-step explanation:
Find the length of the side joining the ends of the 2 shortest sides:
x^2 = 3.4^2 + 5.6^2 - 2*3.4*5.6 cos 113
x^2 = 57.8
x = 7.6.
The area of the quadrilateral is made up up the area of 2 triangles.
Using Hero's formula for the area of a triangle.
Area = √(s(s-a)(s-b)(s-c)) where a b and c are the lengths of the 3 sides and s is the semi-perimeter.
For the smaller triangle, s = (3.4 + 5.6 + 7.6) / 2 = 16.6/2 = 8.3.
So its area = √[8.3(8.3-3.2)(8.3-5.6)(8.3-7.6)]
= √76.8663
= 8.77 yd^2.
For the larger triangle, s = (7.6 + 7.6 + 10.9) / 2 = 13.05 yd.
Area of the larger triangle
= √[13.05(13.05- 7.6) (13.05- 7.6) (13.05- 10.9)]
= √833.378
= 28.87 yd^2.
Total area = 28,87 + 8.77
= 37.64 yd^2.
x2 =m
