Area Calculations and Probability in Geometric Shapes

A circular park has a radius of 10 meters. If a person randomly throws a dart at the park, what is the probability that it lands within a 5-meter radius from the center?

• 0.25

• 0.5

• 0.75

• 0.1

A rectangular garden measures 12 meters by 8 meters. If a butterfly randomly flies within the garden, what is the probability that it lands in a square area of 4 meters by 4 meters located in one corner?

• 1/8

• 1/4

• 1/12

• 1/6

A triangular field has a base of 14 meters and a height of 10 meters. If a bird randomly lands anywhere in the field, what is the probability that it lands in a smaller triangle with a base of 7 meters and a height of 5 meters?

• 0.75

• 0.5

• 0.1

• 0.25

A circular swimming pool has a diameter of 20 meters. If a child randomly swims in the pool, what is the probability that they are within 3 meters of the edge?

• 0.51

• 0.25

• 0.33

• 0.75

A rectangular playground is 30 meters long and 20 meters wide. If a ball is thrown randomly in the playground, what is the probability that it lands in a circular area with a radius of 5 meters located at the center of the playground?

• π / 24 or approximately 0.1309

• π / 30 or approximately 0.1047

• 1/6 or approximately 0.1667

• 1/12 or approximately 0.0833

A square plot of land has an area of 100 square meters. If a rabbit randomly hops around the plot, what is the probability that it hops into a smaller square area of 25 square meters located in one corner?

• 0.25

• 0.5

• 0.1

• 0.75

A circular pizza has a radius of 12 inches. If a person randomly takes a slice from the pizza, what is the probability that the slice contains an area of less than 30 square inches?

• 0.1

• 0.0196

• 0.5

• 0.25

A rectangular room is 15 feet by 10 feet. If a fly randomly flies around the room, what is the probability that it lands on a rug that covers an area of 3 feet by 4 feet?

• 0.25

• 0.08

• 0.15

• 0.05

A triangular piece of land has sides measuring 10 meters, 12 meters, and 14 meters. If a deer randomly grazes in the area, what is the probability that it grazes in a smaller triangle with an area of 20 square meters?

• 0.144

• 0.1

• 0.25

• 0.5

A circular track has a radius of 50 meters. If a runner randomly chooses a point on the track, what is the probability that they are within 10 meters of the center of the track?

• 0.2

• 0.1

• 0.5

• 0.04