Question

What is the area of the shaded region in the figure below?

Answer 1

a. 32π −16
b. 16π − 16
c. 32π − 32
d. 16π − 32

Answer 2

@jim_thompson5910

Answer 3

Hint:

Area of Shaded Region = (Area of Circular Pie Shaped Piece) - (Area of Triangle)

Answer 4

@jim_thompson5910 i don't get it..

Answer 5

http://www.mathsisfun.com/geometry/images/circle-sector-area.gif

Answer 6

and I assume you know what the Area of a triangle is, if not, check your formulas sheet

Answer 7

i still don't understand @jdoe0001

Answer 8

your graphic shows an "arc" or so-called "sector of a circle", you use the formula there
THEN
you use the triangle formula to get the non-shaded triangular area, and substract that form the sector's

Answer 9

i get that but it's the equation that's confusing me

Answer 10

ok, lemme rewrite it

Answer 11

$$
\cfrac{\color{red}{\theta} r^2}{2}\\
\textrm{mind you that } \color{red}{\theta} \text{ should in radians}
$$

Answer 12

in this case \(\large 90^o = \frac{\pi}{2} \)

Answer 13

okay so should i cross multiply that?

Answer 14

@jdoe0001

Answer 15

$$
\cfrac{\color{red}{\theta} r^2}{2} \implies \cfrac{\color{red}{\frac{\pi}{2}} r^2}{2} \implies \cfrac{\color{red}{\pi} r^2}{4}
$$