In this problem we need to find the apothem and the length of the side before we can find the area of the entire polygon. Each central angle for a regular pentagon is <span><span><span>360∘</span>5</span>=<span>72∘</span></span><span>. So, half of that, to make a right triangle with the apothem, is </span><span>36∘</span><span>. We need to use sine and cosine. </span><span><span>sin<span>36∘</span></span><span>4sin<span>36∘</span></span><span>8sin<span>36∘</span></span>n</span><span><span>=<span><span>.5n</span>4</span></span><span>=<span>12</span>n</span><span>=n</span><span>≈4.7</span></span><span><span> cos<span>36∘</span>=<span>a4</span></span><span>4cos<span>36∘</span>=a</span><span>a≈<span>3.24 </span></span></span>Using these two pieces of information, we can now find the area. <span>A=<span>12</span>(3.24)(5)(4.7)≈38.07 unit<span>s^2</span></span><span>.</span>
