452,580 views
20 votes
20 votes
find the area of the white region ...blue region has a 150 degree triangle with 7cm side and the circle has a radius of 7

User Listboss
by
2.8k points

1 Answer

8 votes
8 votes

First, let's find the area circular sector:


A=(r^2\theta)/(2)

Where:

r = radius = 7cm

θ = angle (in radians) = 5/6 π

so:


\begin{gathered} A=(7^2((5)/(6)\pi))/(2) \\ A=(245)/(12)\pi \end{gathered}

Now, let's find the area of the triangle, that triangle is an isosceles triangle, so, we can use the following formula in order to find its area:


\begin{gathered} At=(1)/(2)s^2\cdot\sin (\theta) \\ \end{gathered}

where:

s = one of the equal sides = 7

θ = angle = 150

so:


\begin{gathered} At=(1)/(2)(7^2)\sin (150) \\ At=(49)/(4) \end{gathered}

Therefore, the area of the white region will be, the area of the circular sector minus the area of the isosceles triangle, so:


Area_{\text{ }}of_{\text{ }}the_{\text{ }}white_{\text{ }}region=(245)/(12)\pi-(49)/(4)=51.9cm^2

User Gerd Castan
by
3.2k points