The area of sector MAG is 111 square units, if the diameter MP = 26, m∠GAI = 30° and radii are GA and AI.
Step-by-step explanation:
The given is,
Diameter MP = 26
m∠GAI = 30°
GA and AI are radii
In the given question diagram is not given, we attach the diagram.
Step:1
Formula for area of semi circle,
[tex]A_{Bottom circle} = \frac{\pi r^{2} }{2}[/tex].............................(1)
where, r - radius of circle
From given, D = 26 units
r = [tex]\frac{d}{2}[/tex]
[tex]r = \frac{26}{2}[/tex]
r = 13
Equation (1) becomes,
[tex]A_{Bottom circle} = \frac{\pi 13^{2} }{2}[/tex]
[tex]= \frac{\pi (169)}{2}[/tex]
= (3.1415)(84.5) (∵ [tex]\pi = 3.1415[/tex] )
= 265.456 square units
[tex]A_{Bottom circle} =[/tex] 265.456 square units
Step:2
Ref attachment,
Area of MAG = Area of PAI (From figure)
Area of semi circle = Area of MAG + Area of GAI + Area of PAi
= 2 ( Area of MAG) + Area of GAI
Above equation modified to,
2 (Area of MAG) = Area of semi circle - Area of GAI
Step:3
The Area of GAI is [tex]\frac{1}{6}[/tex] times of Area of semi circle
(Six times of 30° equal to 180°)
Area of GAI = [tex]\frac{1}{6}[/tex] × Area of semi circle
= [tex]\frac{1}{6}[/tex] × 265.456
Area of GAI = 44.2423 square units
From step 2,
2 (Area of MAG) = 265.456 - 44.2423
= 221.213
Area of MAG = [tex]\frac{221.213}{2}[/tex]
= 110.60677
Area of MAG ≅ 111 square units
Result:
The area of sector MAG is 111 square units, if the diameter MP = 26, m∠GAI = 30° and radii are GA and AI.
