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Find the area of a regular heptagon with an apothem of 5 cm. Round to the nearest tenth.

Find The Area Of A Regular Heptagon With An Apothem Of 5 Cm Round To The Nearest Tenth class=

Sagot :

Answer:

[tex]84.3\text{ cm}^2[/tex]

Explanation:

Here, we want to calculate the area of the regular heptagon

Mathematically, we use the formula below:

[tex]A\text{ = a}^2n\text{ tan\lparen}\frac{180}{n})[/tex]

where:

a is the length of the apothem which is 5 cm

n is the number of sides of the polygon which is 7 (heptagon is a 7-sides polygon)

Substituting the values, we have it that:

[tex]\begin{gathered} A\text{ = 5}^2\times7\text{ }\times\text{ tan }\frac{180}{7} \\ \\ A\text{ = 84.3 cm}^2 \end{gathered}[/tex]

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