From the information given,
A is the center of the circle
AB is the radius
AB = 5
BC is the diameter of the circle
BC = 2 x radius = 2 x 5 = 10
Area of shaded region = Area of circle - area of triangle
The formula for calculating the area of a circle is
Area = πr^2
where
r is the radius of the circle
Area of circle = 3.14 x 5^2 = 78.5
Triangle BAD is congruent to triangle CAD
Thus, BD = CD
Triangle BDC is a right triangle
We would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
hypotenuse = BC = 10
one leg = other leg = BD = CD
Thus,
10^2 = BD^2 + CD^2 = 2BD^2
100 = 2BD^2
BD^2 = 100/2 = 50
BD = √50
BD = 5√2
The formula for calculating the area of a triangle is
Area = 1/2 x base x height
height = 5√2
base = 5√2
Area = 1/2 x 5√2 x 5√2 = 1/2 x (5√2)^2
Area of triangle = 25
Area of shaded region = 78.5 - 25
Area of shaded region = 53.5 cm^2