To find the area of a sector of a circle in terms of π having the angle in degrees you use the next formula:
[tex]A=\frac{\theta}{360}\cdot\pi\cdot r^2[/tex]r is the radius
To find area of sector MAG:
1. Find the angle of the sector MAG.
The semicircle has an angle of 180° and it is divided into 3 sectors MAG, GAI, and IAP.
As the arcs MG and IP are congruents (have the same measure) the angles of the sectors MAG and IAP are also congruent.
[tex]\begin{gathered} m\angle\text{MAG}+m\angle\text{GAI}+m\angle\text{IAP}=180 \\ \\ m\angle MAG=m\angle IAP \\ m\angle GAI=30 \\ \\ 2m\angle MAG+m\angle GAI=180 \\ 2m\angle MAG+30=180 \end{gathered}[/tex]Use the equation above to find the measure of angle MAG:
[tex]\begin{gathered} 2m\angle MAG=180-30_{} \\ 2m\angle MAG=150 \\ m\angle MAG=\frac{150}{2} \\ \\ m\angle MAG=75 \end{gathered}[/tex]2. Find the area of sector MAG:
Angle 75°
radius= half of the diameter (26/2 = 13)
r=13
[tex]\begin{gathered} A=\frac{75}{360}\cdot\pi\cdot(13)^2 \\ \\ A=\frac{75}{360}\cdot\pi\cdot169 \\ \\ A=\frac{12675}{360}\pi \\ \\ A=\frac{845}{24}\pi \\ \\ A\approx35.21\pi \\ \\ A\approx110.61 \end{gathered}[/tex]The exact area of the sector MAG is 845/24 π units squared.
Rounded to the nearest hundredth 35.21 π units squared or 110.61 units squared
