Question

find the area of each of the following regular polygons.
a.
b.

a. the area of the regular hexagon is ( 54sqrt{3} cm^{2}).
(simplify your answer. type an exact answer, using radicals as needed.)
b. the area of the regular triangle is
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).

Step2: Identify the base and height of the regular triangle

For the regular triangle, the base \(b = 8\space cm\) and the height \(h=4\sqrt{3}\space cm\).

Step3: Substitute the values into the formula

Substitute \(b = 8\) and \(h = 4\sqrt{3}\) into \(A=\frac{1}{2}\times b\times h\).

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Answer:

\(16\sqrt{3}\space cm^{2}\)