Question

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Answer 1

Area of DEABC = 30100 m²

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

=
`(1)/(2)(EG)(GD)`

=
`(1)/(2)(120)(100+80)`

=
`60* 180`

= 10800 m²

Area of figure (2) = Area right triangle AGE

=
`(1)/(2)(EG)(AG)`

=
`(1)/(2)(120)(30+50)`

= 60 × 80

= 4800 m²

Area of figure (3) = area of triangle AHB

=
`(1)/(2)(AH)(HB)`

=
`(1)/(2)(50)(50)`

= 1250 m²

Area of figure (4) = Area of trapezoid BCFH

=
`(1)/(2)(b_1+b_2)h`

=
`(1)/(2)(HB+FC)(HF)`

=
`(1)/(2)(50+100)(30+80)`

=
`(1)/(2)(150)(110)`

= 8250 m²

Area of figure (5) = Area of right ΔDFC

=
`(1)/(2)(DF)(FC)`

=
`(1)/(2)(100)(100)`

= 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