Question

FInd the area of shaded region

Answer 1

57.51

Explanation:

Each angle of a polygon with n sides is given by:

`((n-2)*180)/(n)\\ \\= ((8-2)*180)/(8)\\\\=(6*180)/(8)\\ \\=135`

The shaed are is the sum of area of 4 triangles

Since the triangle has two sides equal, it is an isosceles triangle

The area of an isosceles triangle with an included angle is:

`(1)/(2)a^2 sin(\theta)`

Since there are 4 tiangles, the total area is :

`4((1)/(2)a^2 sin(\theta))\\\\=4((1)/(2)9^2 sin(135))\\\\= 9^2 sin(135)\\\\= 81* 0.71\\\\= 57.51`