The area of square is 4 in^2, the area of small rectangle is 3 in^2, the area of large rectangle is 13 in^2 and the total area of the polygon is 20 in^2.
A square is a quadrilateral. It is closed, two-dimensional shape with 4 equal sides and four right (90°) angles.
A rectangle is also a quadrilateral, 2-D shape whose opposite sides are equal and parallel with four angles equal to 90 degrees.
For the given situation,
The polygonal figure has been decomposed into one square and two rectangles.
Square:
The length of the square,s = 2 in
The formula of area of square is
[tex]A=s^{2}[/tex]
⇒ [tex]A=(2)(2)[/tex]
⇒ [tex]A=4[/tex] square in.
Small rectangle:
The length of the rectangle,l = 2 in
The breadth of the rectangle,b = 1.5 in
The formula of area of rectangle is
[tex]Area = lb[/tex]
⇒ [tex]Area = (2)(1.5)[/tex]
⇒ [tex]Area = 3[/tex] square in.
Large rectangle:
The length of the rectangle,l = 6.5 in
The breadth of the rectangle,b = 2 in
⇒ [tex]Area = (6.5)(2)[/tex]
⇒ [tex]Area=13[/tex] square in
Thus the total area of the polygon is the sum of all areas of square and rectangles,
⇒ [tex]Total area=4+3+13[/tex]
⇒ [tex]Total area=20[/tex] square in.
Hence we can conclude that the area of square is 4 in^2, the area of small rectangle is 3 in^2, the area of large rectangle is 13 in^2 and the total area of the polygon is 20 in^2.
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