Answer:
Area of DEABC = 30100 m²
Step-by-step explanation:
Area of the given composite figure will be the sum of areas of 5 different figures.
Area of figure (1) = Area of right triangle ΔEGD
= [tex]\frac{1}{2}(EG)(GD)[/tex]
= [tex]\frac{1}{2}(120)(100+80)[/tex]
= [tex]60\times 180[/tex]
= 10800 m²
Area of figure (2) = Area right triangle AGE
= [tex]\frac{1}{2}(EG)(AG)[/tex]
= [tex]\frac{1}{2}(120)(30+50)[/tex]
= 60 × 80
= 4800 m²
Area of figure (3) = area of triangle AHB
= [tex]\frac{1}{2}(AH)(HB)[/tex]
= [tex]\frac{1}{2}(50)(50)[/tex]
= 1250 m²
Area of figure (4) = Area of trapezoid BCFH
= [tex]\frac{1}{2}(b_1+b_2)h[/tex]
= [tex]\frac{1}{2}(HB+FC)(HF)[/tex]
= [tex]\frac{1}{2}(50+100)(30+80)[/tex]
= [tex]\frac{1}{2}(150)(110)[/tex]
= 8250 m²
Area of figure (5) = Area of right ΔDFC
= [tex]\frac{1}{2}(DF)(FC)[/tex]
= [tex]\frac{1}{2}(100)(100)[/tex]
= 5000 m²
Therefore, area of composite figure = Area of (1) + Area of (2) + Area of (3) + Area of (4) + Area of (5)
= 10800 + 4800 + 1250 + 8250 + 5000
= 30100 m²
