Question

GEOMETRY: Find the area of the shaded region.

Answer 1

i have an answer but im not sure :) just want to check, pls help me :)

Answer 2

any measurements given? like radius or such?

Answer 3

notice, the area of the sector minus the are of the right triangle gives you the area of the segment. the total area you desire is 2 times the area of the segment.

Answer 4

@jdoe0001 it's in the picture, r =1 :)

Answer 5

the radius is 1. so the area of the sector is pi/4, the area of the triangle is 1/2 and the area of the segment is pi/4 - 1/2 = (pi - 2)/4 and the total area would be ...

Answer 6

oops the area of the sector is pi/2

so the area of the segment is (pi - 1)/2 and the total area is...

Answer 7

ohh, so im wrong. haha my answer is pi/2 - 1

Answer 8

well, uhm thanks btw! @pgpilot326 :)

Answer 9

@pgpilot326 may i ask? :) so the area we're looking for is times two of the shaded part of this: ?

Answer 10

you got it

Answer 11

yeah so doubling (pi - 1)/2 is pi - 1.

Answer 12

you got it right.

Answer 13

@pgpilot326 why is sector pi/2? isnt it pi/4?

Answer 14

r^2 * theta (in radians) is the area of a sector with central angle theta.

Answer 15

Area of the Sector = 1/2 r squared (teta)

right?

Answer 16

oops, you're right... it's theta/2

Answer 17

so it's pi/4 :)

Answer 18

2 (pi/4 - 1/2) ** doubling the area from my second pic**

pi/2 -1 :) !

Answer 19

sorry, going too fast. so yeah, the original

area of segment = pi/4 - 1/2 = (pi - 2)/4 and total area is (pi - 2)/2

Answer 20

haha thanks again @pgpilot326 :)

Answer 21

sorry 'bout that!

Answer 22

yah it's ok :)

Answer 23

just in case...

http://www.mathsisfun.com/geometry/circle-sector-segment.html

Answer 24

thanks!