Three equilateral triangles with side lengths 3,6 and 4, respectively, are joined as shown. Find the area of the shaded region.

Guest Dec 21, 2019

#1**+2 **

Note that in both shaded triangles.....the angles that are touching the base of the figure must = 60°

So the shaded area ( a triangle) on the left = (1/2) (6)(3)sin(60°)

And the shaded area on the right (a riangle) = (1/2) * (6) (4) sin (60°)

So....the total area of the two shaded regions =

(1/2)(6)sin(60°) [ 3 + 4 ] =

3(√3/2) [ 7] =

21√3

_____ units^2 ≈ 18.19 units^2

2

CPhill Dec 21, 2019