Respuesta :

The angle between the lines in 90 degrees so the area of the  whole sector is 1/4 of a circle

= 1/4 * pi * 8^2

The area of the triangle = 1/2 * 8 * 8 = 32

so area of the shaded segment =  (16pi - 32) in^2

choice 1.
calculista

Answer:

the answer is the first option

[tex](16\pi\ -32)\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of the shaded portion of the circle is equal to the area of a quarter circle minus the area of the right triangle

Step 1

Find the area of a quarter circle

[tex]A=\frac{1}{4}\pi r^{2}[/tex]

we have

[tex]r=8\ in[/tex]

substitute

[tex]A=\frac{1}{4}\pi (8)^{2}=16\pi\ in^{2}[/tex]

Step 2

Find the area of the right triangle

we know that

the area of the triangle is equal to

[tex]A=\frac{1}{2}bh[/tex]

in this problem we have

[tex]b=h=8\ in[/tex]

substitute

[tex]A=\frac{1}{2}(8)^{2}=32\ in^{2}[/tex]

Step 3

Find the area of the shaded portion

Remember that

The area of the shaded portion of the circle is equal to the area of a quarter circle minus the area of the right triangle

[tex]A=(16\pi\ -32)\ in^{2}[/tex]