An arc subtends an angle of 105°at the center of a circle of radius 6cm. Find the length of the arc (2). Length of the chord subtended at such angle (3). Perimeter of such sector and segment (4). Area of such sector and segment

Well I am not going to do it for you but to get started

105 degrees is part way around, how much of a part?
105 / 360 = 0.2917
so
the length of the arc will be
0.2917 * 2 pi R= 0.2917 * 2 * 3.14 * 6 = 11 cm

The rest of it is just an isoceles triangle with equal legs of 6 cm and included 105 deg angle. That makes the other two angles (180 - 105) /2 =
37.5 deg . I think you can find the base and altitude etc.

Did you know?

Did you know that to find the length of an arc subtending an angle in a circle, you can use the formula (angle/360) x 2πr? In this case, with an angle of 105° and a radius of 6cm, the length of the arc is approximately 19.63cm. Furthermore, the length of the chord subtended by the same angle can be found using the formula 2r sin(angle/2). For this scenario, the length of the chord is approximately 10.21cm. To calculate the perimeter of the sector formed by the arc and two radii, simply add the length of the arc to twice the radius. Therefore, the perimeter is about 31.63cm. Additionally, the perimeter of the segment formed by the arc and one of its radii is found by adding the length of the arc to the length of the chord. In this case, the perimeter of the segment is approximately 29.84cm. Lastly, the area of the sector can be calculated using the formula (angle/360) x πr². Thus, the approximate area of the sector is 57.92cm². Similarly, the area of the segment can be found by subtracting the area of the triangle formed by the chord and the two radii from the area of the sector.