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.
and explain plis

Answer 1

9514 1404 393

Explanation:

The figure shows a regular pentagon with the radius and the length of one side given. The Pythagorean theorem to find the missing side of the right triangle whose given sides are the pentagon radius and half the side length. That missing side is the apothem of the pentagon. As with any regular polygon, the area of this pentagon will be half the product of the perimeter and the apothem. The perimeter of a pentagon is 5 times the side length. All dimensions are in feet, so the area will be in square feet.

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Additional comment

The working out was not requested, but here it is, anyway.

  a = √(40.8² -(48/2)²) = √1088.64 ≈ 32.99 . . . feet

  P = 5(48 ft) = 240 ft

  A = (1/2)Pa = (1/2)(240 ft)(32.99 ft) = 3959.3 ft²

Note that the radius has been rounded down to the nearest tenth. If the full-accuracy value were used, the area would be found to be 3963.98 ft².