The area of the figure shown in the picture is 22 squares if the approximate side length of the figure is 3.5 in option (C) is correct.
What is a regular polygon?
A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
A pentagon is shown in the coordinate plane:
Let's assume all side of the pentagon is equal:
The measure of the diagonal of the pentagon d = (1 + √5)a/2
a is the side length of the pentagon.
a = 3.5 (approximate)
d = (1 + √5)3.5/2
d = 5.663 in
The area of the pentagon:
[tex]\rm A = \dfrac{1}{4}(\sqrt{5(5+2\sqrt{2})})a^2[/tex]
Plug a = 3.5 in
[tex]\rm A = \dfrac{1}{4}(\sqrt{5(5+2\sqrt{2})})(3.5)^2[/tex]
A = 21.07 ≈ 22 square in
Thus, the area of the figure shown in the picture is 22 squares if the approximate side length of the figure is 3.5 in.
Learn more about the regular polygon here:
brainly.com/question/11810316
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