Question

1.
Esther's company has been contracted to lay carpet in a room at a new observatory. The floor plan for the room is in the shape of a regular pentagon and has measurements as shown in the diagram below.






Use complete sentences to explain how to find the area that Esther's company will carpet? Do not forget the units in your final answer.

A word bank has been provided. Make sure to use only the appropriate words related to this problem.

Answer 1

The value of the area that Esther's company will carpet is : A = 4750.56 ft².

 To determine the value of the area that Esther's company will carpet, the Pythagorean theorem is applied to calculate the apothem and then the formula for the area of ​​a regular polygon, in this case a pentagon, is applied as follows:

  L = 48 ft

 A=?

  Applying the Pythagorean theorem results:

      ( 24ft)² +a² = (40.8ft)²

    The value of the apothem is:

        a = 32.99 ft

       

  Formula of the area of ​​a regular polygon ( pentagon) :                                                                                                                            

    A= 6*L*a/2

   A = 6* 48ft*32.99 ft/2

   A = 4750.56 ft²

The complete statement with its corresponding figure is attached.