Question

What percent of the figure is shaded? The large figure is a square, and each arc is one-fourth of a circle.

Answer 1

$A$Answer:

Step-by-step explanation:

Hi there,

To get started, notice there are four sections not shaded. Since the shape is perfectly curved and each point along the arc is equidistant from that arc's corner of the shape, this means each non-shaded section is a quarter of a circle. Since we know the square's full area,

$A=s^{2}=(10cm)^{2} =100 \ cm^2$

This will be our denominator,  since we are comparing shaded area to total area. The total shaded area is 4 times the area of a quarter-circle:

$A_w=4*A_Q_u_a_r_t_e_r = 4*(1/4)(\pi r^2)=\pi r^2$

Notice, this is just the area of a circle! However, keep in mind the radius of one of the quarter circles is half the side length of the square:

$r=\frac{1}{2} s=\frac{1}{2}(10cm)=5cm$

Now, we want the shaded area. However, the white area is the non-shaded portion. We know the total area contains both shaded and non shaded:

$A_t_o_t_a_l=A_w + A_s$

Solve for area shaded:

$A_s= A_t_o_t_a_l-A_w$

Now

A%$=\frac{A_t_o_t_a_l-A_w}{A_t_o_t_a_l} *100$ %  

Now, we can just go ahead and plug in!

A% = $\frac{100cm^2-(\pi(5cm)^2)}{100cm^2} *100$  =21.46 %

Thus, the shaded area percent is 21.46%.

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