Question

A floor plan is shown. A small rectangle with height 150 meters and length 200 meters is connected to a larger rectangle with height 350 meters and length 200 meters. A semicircle is on top of the second larger rectangle.
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 semicircle is
.

The area of the office shown in the floor plan
.

Answer 1

Radius: 100 m.

Area: rectangles = 150·200 + 350·200 = 30,000 + 70,000 = 100,000 m².
Semicircle area = (1/2)πr² = 1/2·π·100² = 5,000π m².
Total area = 100,000 + 5,000π ≈ 115,708 m².

Yes — 115,708 m² > 110,000 m², so there is enough space.