Question

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.

Answer 1

• 3960 ft²

Explanation:

The pentagon has been split into 5 congruent triangles.

Each triangle has area of:

• 1/2*48*
  `√(40.8^2 - (48/2)^2)` = 24*
  `√(1088.64)` = 24*33 = 792 ft²

The area of the room is:

• 792*5 = 3960 ft²