Question

What is the area of a shape with points a 5 -8 b 11, -8 c 11,0 d 6,-3 e 4,-3

Answer 1

Area of the given figure is 51.5 square units.

Explanation:

Area of rectangle OCBH = Length × width

= 11 × 8

= 88 square units

Area of trapezoid OGEF =
`(1)/(2)(b_1+b_2)* h`

=
`(1)/(2)(\text{GE+OF)}* (\text{OG})`

=
`(1)/(2)(3+6)* 4`

= 18 units²

Area of trapezoid GCDE =
`(1)/(2)(\text{GC+DE)}* (\text{GE})`

=
`(1)/(2)(7+2)* 3`

= 13.5 units²

Area of triangle AFH =
`(1)/(2)(\text{Base})* (\text{Height})`

=
`(1)/(2)(5)(2)`

= 5 units²

Area of polygon ABCDEF = Area of rectangle CBHO - (Area of trapezoid OGEF + Area of trapezoid GCDE + Area of triangle AFH)

= 88 - (18 + 13.5 + 5)

= 88 - 36.5

= 51.5 units²

Therefore, area of the given polygon is 51.5 units²