Question

If the cost of the carpeting is $15 per square meter, find the total cost of carpeting the floor of the room whose shape is a regular pentagon shown below. 
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Answer 1

SOLUTION:-

To find the total cost of carpeting the floor of the room, we have to know its area. Because the floor of the room is in the shape of regular pentagon (regular polygon), we can use the formula for area of a regular polygon to find the area of the floor.    

Formula for area of a regular polygon :

➞  1/2 ×apothem × perimeter of polygon ----(1)

In the above regular pentagon, apothem is 4 m 

The perimeter of a regular polygon is 

⇒  No. of sides ×Length of each side

Therefore, the perimeter of the regular pentagon shown above is 

⇒6×5

⇒30 m

To find the area of the regular pentagon, substitute 4 for apothem and 30 for perimeter in the formula (1). 

1) ----> =  1/2 × 4 ×30

=  60 m

So, the area of the floor is 60 square meters.

The cost of carpeting is $15 per square meter. 

Then, the total cost of carpeting for 60 square meters : 

=60×15

=900

So, the total cost of carpeting the floor of the room is $900