Answer:
Isosceles trapezoid (25 in²) > Hexagon (22 in²) > Parallelogram (21 in²) > Rhombus (20 in²)
step-by-step explanation:
Area of Rhombus,
= Base Length x 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 Trepezoid
= ( 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)
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