The area of the polygon is 35.5 square units. Option C shows the correct area of the given polygon.
The area can be defined as the amount of space used by a two-dimensional object.
Given that ABEDFG is a polygon. As shown in the attachment, we divided the polygon into 4 different parts.
In triangle EDC, EC = 3, DC = 4.
Area = [tex]\dfrac { 1}{2} \times EC \times DC[/tex]
Area = [tex]\dfrac {1}{2} \times 3\times 4[/tex]
Area = 6
In triangle GFD, height = 2, base = 7.
Area = [tex]\dfrac { 1}{2} \times base \times height[/tex]
Area = [tex]\dfrac {1}{2} \times 2\times 7[/tex]
Area = 7
In triangle GDA, AD = 3, GD = 7.
Area = [tex]\dfrac { 1}{2} \times AD \times GD[/tex]
Area = [tex]\dfrac {1}{2} \times 3\times 7[/tex]
Area = 10.5
In rectangle ABCD, DC = AB = 4, CB = AD = 3.
Area = [tex]AB\times AD[/tex]
Area = [tex]4\times 3[/tex]
Area = 12
The area of the polygon is the sum of all the areas.
Area = 6 + 7 + 10.5 + 12
Area = 35.5 square units.
Hence we can conclude that the area of the polygon is 35.5 square units. Option C shows the correct area of the given polygon.
To know more about the area, follow the link given below.
https://brainly.com/question/1631786.
