Question

What is the approximate area of the regular pentagon?

Answer 1

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:

$h=\sqrt{12^2-(\frac{L}{2})^2}=\sqrt{12^2-(\frac{14.1}{2})^2}=9.7 cm$

The area of each of the 5 triangles is

$A'=\frac{1}{2}Lh$

Therefore, the area of the pentagon is 5 times this area:

$A=5A'=\frac{5}{2}Lh=\frac{5}{2}(14.1)(9.7)=342 cm^2$

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Answer 2

Answer:

342 cm2

Step-by-step explanation:

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