Question

Jacob is constructing a pentagonal tent for his school carnival. The tent has a side length of 5.13 meters. What is the area of the tent? What is the perimeter of the tent? What is the sum of three of the interior angles in the tent once Jacob obtains the value of its area and perimeter?

Answer 1

The tent is pentagonal , this means it has 5 sides. The tent have a side length of 5.13 meters.

The area of the pentagon can be calculated below

`\begin{gathered} \text{area of the tent=}(perimeter* apothem)/(2) \\ \tan \text{ 36=}(2.565)/(a) \\ a=\frac{2.565}{\tan \text{ 36}} \\ a=(2.565)/(0.726542528) \\ a=3.53041962601 \\ \text{perimeter}=\text{ 5.13}*5=25.65\text{ meters} \\ \text{area =}(25.65*3.53041962601)/(2) \\ \text{area}=(90.5445)/(2) \\ \text{area}=45.27225 \\ \text{area}\approx45.27meter^2 \end{gathered}`

Each interior angle of a pentagon is

`\begin{gathered} \text{ interior angle=}(180*3)/(5)=(540)/(5)=108^(\circ) \\ \text{ Sum of thr}ee\text{ interior angles = 108}*3=\text{ }324\text{ degre}e \end{gathered}`