Question

Find the area of the figure shown in the diagram to the nearest hundredth.

A) 16.00 m2
B) 28.57 m2
C) 41.13 m2
D) 49.12 m2

Answer 1

Answer: Choice C) 41.13 square meters

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This figure is a composition of two quarter-circles and a square

Area of quarter circle = (1/4)*(area of circle)
Area of quarter circle = (1/4)*(pi*r^2)
Area of quarter circle = (1/4)*(pi*4^2)
Area of quarter circle = (1/4)*(pi*16)
Area of quarter circle = (1/4)*16*pi
Area of quarter circle = 4pi
There are two quarter circles, so the two circular areas add to 4pi+4pi = 8pi

Area of square = s*s = 4*4 = 16 square meters

Add the square area to the circular area: 8pi+16

Now use a calculator to find 8pi+16 = 41.1327412287183 which rounds to 41.13