Question

find the area of the rectangular field ABCDE where EF, BG and DH are perpendicular to AC . Given AF= 40 m , AG=50 m ,GH=40 m and CH =50.m

Answer 1

Answer:

7225 m²

Step-by-step explanation:

AED is not a straight line as it looks in picture

AC = AG + GH + CH = 140 m

BG = 45 m

Area of ΔABC = (1/2)AC * BG = (1/2)(140)(45) =  3150 m²

Area of ΔAFE = (1/2)AF * FE =  (1/2)(40)(35) =  700 m²

Area of ΔCHD = (1/2)CH * HD =  (1/2)(50)(50) = 1250 m²

FH = AH - AF = AG + GH - AF = 50 + 40 - 40 = 50

Area of Trapezium HDEF = (1/2)(HD + EF) * FH = (1/2)(50 + 35)* 50 = 2125 m²

Total Area of field ABCDE = 3150 + 700  + 1250 + 2125  = 7225 m²