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Frank wants to find the area enclosed by the figure at the right.

The figure has semicircles on each side of a 40-meter-by-40-meter
square. Find the area enclosed by the figure. Use 3.14 for pie.

User Dzoukr
by
5.6k points

1 Answer

7 votes

Answer:

2856 square meters

Explanation:

The area of the figure will be the sum of the areas of the two semicircles with diameter 40 m, and the square with side length 40 m. The areas of the two semicircles will be equal to the area of a circle of the same diameter.

__

The area formula for a circle of diameter d is ...

A = (π/4)d²

The area formula for a square of side length d is ...

A = d²

Then the total area of the figure with side length d is ...

A = (π/4)d² +d² = d²(1 +π/4)

__

For a 40 m side length and the given value of π, the area is ...

A = (40 m)²(1 +3.14/4) = 2856 m²

The area of the figure is 2856 square meters.

User Lannyboy
by
4.2k points