Area of the pentagon: 342 cm2
Step-by-step explanation:
The figure of the pentagon is missing: find it in attachment.
The area of the pentagon can be seen as the area of 5 equal triangles, each of them having a base equal to the length of the side of the pentagon,
L = 14.1 cm
and the height of each triangle can be found by using Pythagorean's theorem:
[tex]h=\sqrt{12^2-(\frac{L}{2})^2}=\sqrt{12^2-(\frac{14.1}{2})^2}=9.7 cm[/tex]
The area of each of the 5 triangles is
[tex]A'=\frac{1}{2}Lh[/tex]
Therefore, the area of the pentagon is 5 times this area:
[tex]A=5A'=\frac{5}{2}Lh=\frac{5}{2}(14.1)(9.7)=342 cm^2[/tex]
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