SOLUTION: Find the area of the shaded figure, rounded to two decimals. (Assume x = 5 and y = 8.) Area = IMAGE BELOW http://www.webassign.net/sprecalc6/6-6-036-alt.gif

Algebra ->  Trigonometry-basics -> SOLUTION: Find the area of the shaded figure, rounded to two decimals. (Assume x = 5 and y = 8.) Area = IMAGE BELOW http://www.webassign.net/sprecalc6/6-6-036-alt.gif      Log On


   

Question 1030249: Find the area of the shaded figure, rounded to two decimals. (Assume x = 5 and y = 8.)
Area =

IMAGE BELOW
http://www.webassign.net/sprecalc6/6-6-036-alt.gif
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Join the third side to form a triangle
The area of the shaded portion = area of outer triangle - area of inner triangle
The outer triangle is an equilateral triangle
since one angle is 60 deg
and the corresponding sides of the angle are equal
area of equilateral triangle = %28sqrt%283%29%2F4%29%2As%5E2
= sqrt(3)/4 * 8^2
=27.71 cm^2
Area of the smaller triangle with sides 5,5,8
Using Herons formula
s= half perimeter = (5+5+8 )/2 = 9
Area of triangle = sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29 where a,b,c are the sides of the triangle
A= sqrt%289%2A%289-5%29%289-5%29%289-8%29%29
= 12 cm^2
Area of shaded portion = difference of areas of the two triangles