A dartboard shaped like a regular octagon has an apothem of 15 inches. The smaller octagon, which is also regular, has an apothem of 8 inches. What is the probability of a randomly thrown dart landing within the shaded region, given that the dart lands inside the larger octagon? Round the answer to the nearest hundredth. (Hint: An apothem is the perpendicular distance from the center of a regular polygon to its side.) A. 0.14 B. 0.15 C. 0.27 D. 0.28

Question

Mathematics

Beatrice Roberts

27 January, 09:04

A dartboard shaped like a regular octagon has an apothem of 15 inches. The smaller octagon, which is also regular, has an apothem of 8 inches. What is the probability of a randomly thrown dart landing within the shaded region, given that the dart lands inside the larger octagon? Round the answer to the nearest hundredth. (Hint: An apothem is the perpendicular distance from the center of a regular polygon to its side.) A. 0.14 B. 0.15 C. 0.27 D. 0.28

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Answers (2)

Know the Answer?

Alayna Becker · Answer 1

C.

.27

Step-by-step explanation:

e2020

Sierra Terry · Answer 2

Assuming that the person throwing the dart is not aiming for any particular part of the dartboard and that all darts thrown at the board don't miss the board, then we can make use of the area to get the probability

So,

P = A1 / (A1 + A2)

The formula for the area of regular octagon is

A = (1/2) (a) (8) (2a tan 180/8)

A = 8 a² tan 180/8

Where a is the apothem. Substituting, the answer would be

C.

0.27