Arrangement of the Areas in order from greatest to least area are:
Isosceles trapezoid (25 in²) > Hexagon (22 in²) > Parallelogram (21 in²) > Rhombus (20 in²)
How to find the Areas of the Polygons?
Area of Rhombus = Base Length * Height (recall that all sides of a rhombus are the same length, hence the base is the same length 5" as the slant height)
= 5" x 4"
= 20 in²
Area of Parallelogram ,
= Base Length x height
= 7" x 3"
= 21 in²
Area of Isosceles Trapezoid
= (2 x area of each triangle ) + Area of rectangular strip
= (2)(1/2)(base of each triangle)(height) + (width of strip)(height of strip)
= (2)(1/2)[ (9-1) / 2 ] (5) + (1)(5)
= (2)(1/2) (4)(5) + (1)(5)
= 20 + 5
= 25 in²
Area of hexagon = Area of Left Rectangle + Area of Right Rectangle
= (length of left rect.)(width of left rect.) + (length of right rect.)(width of right rect.)
= (5)(6-4) + (4)(3)
= (5)(2) + (4)(3)
= 10 + 12
= 22 in²
Hence we can arrange the shapes by decreasing area:
Isosceles trapezoid (25 in²) > Hexagon (22 in²) > Parallelogram (21 in²) > Rhombus (20 in²)