derive the formula for the area of a sector, and then use it to choose all that are correct.
1.
radius = 5 cm
angle = 120°
area = 26.2 cm2
2.
radius = 4 cm
angle = 105°
area = 16.7 cm2
3.
radius = 6 cm
angle = 85°
area = 23.7 cm2
4.
radius = 7
angle = 75°
area = 32.1 cm2

Part A)

Part B) option 1,option 4

Step-by-step explanation:

Part A) Derive the formula for the area of a sector

we know that

The area of circle is equal to

The area of circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of a sector    by a central angle of ∅ degrees

Part B) Verify each case

case 1) we have

radius = 5 cm

angle = 120°

area = 26.2 cm 2

Find the area of the sector and then compare with the value of the given area

assume

substitute the given values

so

The given value of area is correct

case 2) we have

radius = 4 cm

angle = 105°

area = 16.7 cm 2

Find the area of the sector and then compare with the value of the given area

assume

substitute the given values

so

The given value of area is not correct

case 3) we have

radius = 6 cm

angle = 85°

area = 23.7 cm 2

Find the area of the sector and then compare with the value of the given area

assume

substitute the given values

so

The given value of area is not correct

case 4) we have

radius = 7

angle = 75°

area = 32.1 cm 2

Find the area of the sector and then compare with the value of the given area

assume

substitute the given values

so

The given value of area is correct