Question

a new business requires an office space of at least 110,000 square meters. is there enough space in the floor plan shown here? the radius of the semi - circle is blank. the area of the office shown in the floor plan is blank. is greater than what the business needs. is less than what the business needs. is exactly 110,000 square feet. cannot be determined with the information given

Explanation:

Step1: Calculate area of left - top rectangle

The dimensions of the left - top rectangle are $150$m by $(400 - 200)=200$m. The area of a rectangle is $A = l\times w$. So, $A_1=150\times200 = 30000$ square meters.

Step2: Calculate area of middle rectangle

The dimensions of the middle rectangle are $(150 + 200)$m by $200$m. So, $A_2=(150 + 200)\times200=350\times200 = 70000$ square meters.

Step3: Calculate area of right - bottom rectangle

The dimensions of the right - bottom rectangle are $200$m by $400$m. So, $A_3=200\times400 = 80000$ square meters.

Step4: Calculate area of semi - circle

The radius of the semi - circle $r = 200$m. The area of a semi - circle is $A=\frac{1}{2}\pi r^{2}$. So, $A_4=\frac{1}{2}\pi\times(200)^{2}=\frac{1}{2}\pi\times40000 = 20000\pi\approx20000\times3.14 = 62800$ square meters.

Step5: Calculate total area

The total area of the office $A = A_1+A_2+A_3+A_4=30000 + 70000+80000 + 62800=242800$ square meters.

Answer:

Since $242800>110000$, the area of the office shown in the floor plan is greater than what the business needs.