Question 1030249
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 = {{{(sqrt(3)/4)*s^2}}}

= 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(s(s-a)(s-b)(s-c))}}} where a,b,c are the sides of the triangle

A= {{{sqrt(9*(9-5)(9-5)(9-8))}}}

= 12 cm^2

Area of shaded portion = difference of areas of the two triangles