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A rectangular plot has a length of 45 m and a width of 24 m. Another plot is square-shaped with a side of 32 m. Which plot has a larger area and by how much?
Square plot, 64 sq m
Rectangular plot, 108 sq m
Square plot, 124 sq m
Rectangular plot, 16 sq m
Square plot, 64 sq m
Given: Length = 45 m, Width = 24 m for the rectangle; Side = 32 m for the square.
Length = 45 m, Width = 24 m for the rectangle; Side = 32 m for the square.
Arect=l×w,Asq=s2
Multiply dimensions directly and subtract the smaller area from the larger to get the difference instantly.
Mixing up addition with multiplication when calculating area.
Identify dimensions
The rectangle has length 45 m and width 24 m; the square has side 32 m.
l=45 m,w=24 m,s=32 m
Compute rectangle area
Apply the rectangle area formula Arect=l×w.
Arect=45×24=1080 m2
Compute square area
Apply the square area formula Asq=s2.
Asq=322=1024 m2
Compare areas
Subtract the smaller area from the larger to find the difference.
ΔA=Arect−Asq=1080−1024=56 m2
Conclusion
The rectangular plot is larger by 56 m².
Larger plot: Rectangle, Difference=56 m2
None of the options is correct because the rectangular plot has larger area (1080 m²) exceeding the square plot (1024 m²) by 56 m².
Remember that when scaling dimensions by a factor k, area scales by k²; this helps quickly estimate area changes in similar‑shape problems.