Answer:
1. to find the distance to walk around arc UT, you calculate the diameter (distance around the circle) and you divide by 6 since UT is 1/6 of the circle.
the diameter of a circle can be calculated by 2*radius
the radius in the given (from S to T) is 10
2 * 10 = 20/6 = 10/3
10/3 is the distance to walk around UT
2. to find the area of one of the six sectors, you find the area of the whole circle and divide by 6 since you are only finding the area of ONE of the six sectors.
the area of a circle formula is A = πr^2
A = π10^2
A = π100
A= 314
divide by 6 to find the area of one sector
314 / 6 = 157 / 3
the area of one sector is 157/3
3. since you know the radius and the distance of one sector's curve, you can add all of these lengths by addition.
U to S = 10 (radius)
S to V = 10 (radius)
V to W = 10/3 (1/6 of the diameter)
W to X = 10/3 (1/6 of the diameter)
X to U = 20 (radius times 2 since you are going from one edge of the circle to the other)
40 + 20/3 is the distance to walk