Length of the fence of a trapezium shaped field ABCD is 120meter.If BC=48m,CD=17m and AD=40m,find te area of this field.Sde AB is perpendicular to the parallel side AD and BC
Accepted Solution
A:
Answer:The area of the field is [tex]660 m^{2}[/tex]Step-by-step explanation:Given that the measurements are AD = 40 m, CD = 17 m, BC = 48 mIn the given figure, construct Line perpendicular from D to side CB.So the formed figure is rectangle and triangle.The triangle being right angled, applying pythagoras theorm ,[tex]17^{2} = 8^{2} + x^{2}[/tex]Thus, [tex]x^{2} = 289 - 64 = 225[/tex][tex]x = 15 m[/tex]thus, AB = 15 m ( rectangle opposite sides are equal)Thus, Area of trapezium is,[tex]A = (\frac{1}{2})(Sum of parralle sides)(distance between them)[/tex][tex]A = (\frac{1}{2})(40 + 48)(15)[/tex]A = [tex]660 m^{2}[/tex]