Question

barry wants to host an event at a hotel that has four conference rooms. each conference room has a maximum capacity of 150 people, but the hotel limits the capacity to 1 person for every 4 square feet. sketches of the four conference rooms are shown below. which room will stop barry from hosting the event at the hotel? 25 ft 30 ft 36 ft 24 ft 28 ft 28 ft 28 ft 28 ft

Explanation:

Step1: Calculate area of first rectangle

The area formula for a rectangle is $A = l\times w$. For the first rectangle with length $l = 30$ ft and width $w = 25$ ft, $A_1=30\times25 = 750$ square - feet. The capacity $C_1=\frac{750}{4}=187.5$ people.

Step2: Calculate area of trapezoid

The area formula for a trapezoid is $A=\frac{(a + b)h}{2}$, where $a = 24$ ft, $b = 36$ ft and $h = 28$ ft. So $A_2=\frac{(24 + 36)\times28}{2}=\frac{60\times28}{2}=840$ square - feet. The capacity $C_2=\frac{840}{4}=210$ people.

Step3: Calculate area of second rectangle

For the second rectangle with length $l = 28$ ft and width $w = 28$ ft, $A_3=28\times28 = 784$ square - feet. The capacity $C_3=\frac{784}{4}=196$ people.

Step4: Calculate area of semi - circle

The area formula for a semi - circle is $A=\frac{1}{2}\pi r^{2}$, with diameter $d = 28$ ft, so radius $r = 14$ ft. Then $A_4=\frac{1}{2}\pi\times(14)^{2}=\frac{1}{2}\pi\times196 = 98\pi\approx98\times3.14 = 307.72$ square - feet. The capacity $C_4=\frac{307.72}{4}=76.93$ people.

Since the maximum capacity of a room is 150 people and the semi - circle room has a capacity of approximately 76.93 people which is less than 150, and the other rooms have capacities greater than 150, the semi - circle room will stop Barry from hosting the event.

Answer:

The semi - circle room.