Answer:
Area = 113.01 m²
Step-by-step explanation:
From the picture attached,
Area of the quadrilateral ABCD = Area of triangle ABC+ Area of triangle ACD
Construction to be done → Draw a perpendicular from a point A to the opposite side CD
Area of Δ ABC = [tex]\frac{1}{2}(AB)(BC)[/tex]
= [tex]\frac{1}{2}(12)(10)[/tex]
= 60 m²
Area of triangle ACD = [tex]\frac{1}{2}(AE)(CD)[/tex]
From ΔAEC,
sin(29°) = [tex]\frac{AE}{AC}[/tex]
AC = [tex]\sqrt{(12)^2+(10)^2}[/tex] [By Pythagoras theorem]
AC = [tex]\sqrt{244}[/tex]
AC = 15.62 m
Therefore, AE = 15.62sin(29)
= 7.57 m
Area of ΔACD = [tex]\frac{1}{2}(7.57)(14)[/tex]
= 53.01 m²
Area of ABCD = 60 + 53.01
= 113.01 m²
