Geometry Probability Worksheet with Answer Key

Calculate the probability that a randomly thrown dart lands in a shaded region by forming the ratio of shaded area to total area

Transfer the same ratio idea to one dimension, comparing a shaded length such as a 13-unit hypotenuse or a 6π in arc against a total perimeter

Use the relationship shaded area + unshaded area = total area to reach an answer through whichever region is easier to compute

The sheet opens with a blank "Appoint a reader" line, so decide before handing it out whether groups will name that reader or the line will simply be left unused

Answers on the worked pages are given in exact form and then as a decimal, which lets you accept either 16 - 3π over 16 or 0.411 depending on what the class is practising

Problems 12 through 15 sit on the last page and can be assigned separately as a composite-area and right-triangle review without touching the probability items

Geometric probability from area — students compute the shaded-to-total ratio for figures such as a 6 in circle inscribed in a square (36π/144) and four circles packed inside a 24 cm square (576 - 108π over 576).

Working with the complement — problem 6 directs students to decide whether the shaded or unshaded region is easier to calculate, then recover the other from the total 576 cm² square.

Simplifying radicals — item 11 has students reduce √40 to 2√10, √44 to 2√11 and √48 to 4√3, and mark the primes such as √41 and √47 as already simplified.