Question

In the diagram below of circle A, diameter MP = 26, mZGAI = 30° and radii GA and Al are

drawn
30
If MG a TP, find the area of the sector MAG in terms of and approximated to the nearest
hundredth

Answer 1

The area of sector MAG is 111 square units, if the diameter MP = 26, m∠GAI = 30° and radii are GA and AI.

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,

`A_(Bottom circle) = (\pi r^(2) )/(2)`.............................(1)

where, r - radius of circle

From given, D = 26 units

r =
`(d)/(2)`

`r = (26)/(2)`

r = 13

Equation (1) becomes,

`A_(Bottom circle) = (\pi 13^(2) )/(2)`

`= (\pi (169))/(2)`

= (3.1415)(84.5) (∵
`\pi = 3.1415` )

= 265.456 square units

`A_(Bottom circle) =` 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
`(1)/(6)` times of Area of semi circle

(Six times of 30° equal to 180°)

Area of GAI =
`(1)/(6)` × Area of semi circle

=
`(1)/(6)` × 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 =
`(221.213)/(2)`

= 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.