Question

CHECK MY ANSWER!!!!
Given: BC = 10 inches
AC = √50 inches
m∠CBD = 60°
m∠CAD = 90°

https://wca.sooschools.com/media/g_geo_ccss_2016/8/img_overlap2.gif
Calculate the exact area of the shaded region. Show all work for full credit.
My answer-
Area of shaded figure = area of sector CBD + area of sector CAD - area of CBD- area of CAD
= 60/360 * π * 10² + 90/360 * π * (√50)² - √3/4 * 10² - 1/2 (√50)²
= 50π/3 + 25π/2 - 50√3/2 - 50/2
= 175π- 150√3 - 150 = 6 sq/in
Area of sector = x/360 * πr²

Answer 1

@Vocaloid

Answer 2

give me a min and i will help

Answer 3

@sillybilly123 @mhchen would you mind double checking this if you have a chance

Answer 4

Anyone :(

Answer 5

that was really a good question

Answer 6

okay,so before proceeding to solution ,we have to take an assumption
point A is a circumcenter of triangle CED

Answer 7

from there,we conclude that angle BDA is of 90 degrees

Answer 8

so remaining angle would be of 120 degrees

Answer 9

let area of black portion be x
area of orange portion be y
and yellow shaded region is our goal

Answer 10

now, x=area of quad - area of sector CBD
y=area of quad-area of sector CAD

Answer 11

and suppose area of quad be Q

Answer 12

therefore,
area of yellow shaded portion=Q-x-y
=Q-(Q-area of sector CBD)-(Q-area of sector CAD)
=Q-Q+area of sector CBD-Q+area of sector CAD
=area of sector CBD+area of sector CAD-Q

Answer 13

this seems unrealisitic but we have no choice except of doing that :(

Answer 14

you already calculated the area of both sectors,that's very good and now,we have to calculate the area of quad

Answer 15

\(\color{#0cbb34}{\text{Originally Posted by}}\) @loveboy
okay,so before proceeding to solution ,we have to take an assumption
point A is a circumcenter of triangle CED
\(\color{#0cbb34}{\text{End of Quote}}\)
from this and this
http://www.gogeometry.com/problem/p111_orthogonal_circles_elearning.htm
we concluded that angle BDA is of 90 degrees

Answer 16

you have two triangles now,you can easily calculate the areas and then add up and put in the given equation and hence you find your sol

Answer 17

and yeah if you have any prob,please do let me know :)

Answer 18

hope this helps :D