Question

find the area of the shaded segment of the circle. the area of the shaded segment is __ m squared. round to the nearest tenth if needed

Answer 1

Step-by-step explanation

We must compute the area of the yellow triangle of the diagram:

The area of the yellow portion is given by:

`A_Y=A_(CS)-A_(BT.)`

Where:

• Ay = is the area of the yellow portion,

,

• Acs = is the area of the circular sector with angle θ,

,

• Abt = is the area of the blank triangle inside the circular sector of angle θ.

1) Area of the circular sector with angle θ

First, the angle of this circular sector is given by:

`θ=360°-270°=90°.`

The radius of the circular sector is r = 5 m.

The area of the circular sector is given by:

`A_(SC)(θ)=\pi r^2*(θ)/(360°).`

Replacing the values of θ and r, we get:

`A_(SC)(\theta=90°)\cong3.14\cdot(5m)^2*((90°)/(360°))=19.625m^2.`

2) Area of the blank triangle

We see that the blank triangle is a right isosceles triangle with cathetus:

• b = base = 5m,

,

• h = height = 5m.

The area of this triangle is given by:

`A_(BT)=(1)/(2)\cdot b\cdot h=(1)/(2)\cdot(5m)\cdot(5m)=12.5m^2.`

3) Area of the yellow portion

Replacing the values found above in the equation of the yellow portion, we get:

`A_Y\cong19.625m^2-12.5m^2=7.125m^2.`Answer

The area of the yellow portion is approximately 7.125 m².