Find the area of the shaded figure rounded to two decimals A

Find the area of the shaded figure, rounded to two decimals. (Assume x = 4 and y = 10°)

Solution

Here we have two isosceles triangles.

So first we need to find the height .

h²=y²-(x/2)²

h²= 100-(4/2)^2 = 100-4=96

h= 4sqrt 4

Area= (1/2)x h = (1/2)4(4 sqrt4) = 8 sqrt 6

And we have 2 triangles

Therefore area of two triangles= 2*8 sqrt6 =16 sqrt 6= 39.19