How do the areas of the parallelograms compare? The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.The area of parallelogram 1 is 2 square units greater than the area of parallelogram 2.The area of parallelogram 1 is equal to the area of parallelogram 2.The area of parallelogram 1 is 2 square units less than the area of parallelogram 2.
Accepted Solution
A:
see the attached figure to better understand the problemStep [tex]1[/tex]Find the area of the parallelogram [tex]1[/tex]Find the area of the complete square and subtract the area of the four trianglessoArea of the complete square[tex]A=6^{2}=36\ unit^{2}[/tex]Area of the four triangles[tex]A=4*[\frac{1}{2}*2*4]=16\ unit^{2}[/tex]Area of the parallelogram [tex]1[/tex][tex]A1=36\ unit^{2}-16\ unit^{2}=20\ unit^{2}[/tex]Step [tex]2[/tex]Find the area of the parallelogram [tex]2[/tex]Find the area of the complete rectangle and subtract the area of the four trianglessoArea of the complete rectangle[tex]A=4*8=32\ unit^{2}[/tex]Area of the four triangles[tex]A=2*[\frac{1}{2}*2*6]+2*[\frac{1}{2}*2*2]=16\ unit^{2}[/tex]Area of the parallelogram [tex]2[/tex][tex]A2=32\ unit^{2}-16\ unit^{2}=16\ unit^{2}[/tex]Step [tex]3[/tex]Compare the areas[tex]A1=20\ unit^{2}[/tex][tex]A2=16\ unit^{2}[/tex][tex]A1-A2=20-16=4\ unit^{2}[/tex][tex]A1=A2+4\ unit^{2}[/tex]thereforethe answer is the option The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.