Question

The diagram shows the floor plan of a hotel lobby. Carpet costs $3 per square foot. How much will it cost to carpet the lobby?

Answer 1

Answer:

It will cost $ 3348 to carpet the lobby.

Step-by-step explanation:

Refer the attached figure

AB divides the figure into two congruent trapezium

Height of trapezium = 15.5 feet

Parallel sides = 30 feet and 42 feet

Area of one trapezium = $\frac{1}{2} \times \text{Sum of parallel sides} \times Height$

Area of one trapezium = $\frac{1}{2} \times (30+42) \times15.5$

                                      = $558 ft^2$

So, Area of both trapeziums = $558 \times 2 = 1116 ft^2$

So, Total Area of the floor is 1116 sq.feet.

Cost of carpet of 1 sq.ft. = $3

Cost of carpet of 1116 sq.ft. = $1116 \times 3 =3348$

Hence it will cost $ 3348 to carpet the lobby.

Answer 2

If you were to take both halves of the carpet and place them on top of each other you can see that the two triangle sections would cover each over up and fill in to make a rectangle. So first, lets compute the size of the middle section, then we will compute the size of the end pieces.

The center section of the carpet is 30 ft x 31 ft = 930 sq ft

The ends of the carpet are 12 ft x 15.5 ft = 186 sq ft

Since there are two side to the carpet like this we multiply this by 2
186 * 2 = 372 sq ft

Adding these two values together gives 

930 + 372 = 1302 sq ft