Shaded area is 40 pi cm squared. Find r

r = 10 cm

Step-by-step explanation:

The formula for determining the area of a sector is expressed as

expressed as

Area of sector = θ/360 × πr²

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

θ = 144°

Area of sector = 40π

Therefore,

40π = 144/360 × π × r²

40π × 360 = 144 × π × r²

14400π = 144πr²

Dividing through by π, it becomes

1440 = 144r²

r² = 14400/144

r² = 100

r = √100

r = 10 cm

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc