Question

1.Which explanation justifies how the area of a sector of a circle is derived?

Determine how many triangles can fit into a circle. Divide 360° by the number of triangles. Multiply the quotient by ​the area of the circle​ .

Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply ​the area of the circle​ by this fraction.

Determine the degree of the sector. Divide by 180° and then multiply it by the area of the triangle the sector is in.

Partition the circle into unit squares. Determine the area of the sector and multiply the area by the degree of the circle.

Answer 1

the correct answer is
2) Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply ​the area of the circle​ by this fraction.
area of the circle is calculated by;
area = πr² , where r- radius of circle
the central angle of a circle is 360°. Area of the circle is calculated for central angle of 360°.
Sector is when 2 arms/ radii enclose a central angle between them.
area for 360° = πr²
area for 1 ° = area/ 360
area for central angle of sector = area * angle/ 360
the angle of sector is divided by 360 and taken as a fraction .this fraction of the total area of the circle is taken as the area of the sector.