Question

1. choose efficient methods 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 π.

Explanation:

Step1: Analyze the figure's components

The figure consists of a 40m×40m square and four semicircles (which can be combined into two full circles). First, find the area of the square. The formula for the area of a square is \( A_{square} = s^2 \), where \( s = 40 \) m. So, \( A_{square} = 40^2 = 1600 \) \( m^2 \).

Step2: Find the radius of the semicircles

The diameter of each semicircle is equal to the side length of the square, 40 m. So the radius \( r = \frac{40}{2} = 20 \) m.

Step3: Calculate the area of the two full circles (from four semicircles)

The formula for the area of a circle is \( A_{circle} = \pi r^2 \). We have two circles, so total area of circles is \( 2 \times \pi r^2 \). Substituting \( \pi = 3.14 \) and \( r = 20 \) m: \( 2 \times 3.14 \times 20^2 = 2 \times 3.14 \times 400 = 2512 \) \( m^2 \).

Step4: Find the total area of the figure

Add the area of the square and the area of the two circles: \( A_{total} = A_{square} + A_{circles} = 1600 + 2512 = 4112 \) \( m^2 \).

Answer:

The area enclosed by the figure is \( \boldsymbol{4112} \) square meters.