Question

A square with sides measuring 5 millimeters each is drawn within the figure shown. A point within the figure is randomly selected.

What is the approximate probability that the randomly selected point will lie inside the square?

5.3%

8.4%

13.3%

18.1%

Answer 1

• C) 13.3%

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Area of square with side of 5 mm is:

• A = a² = (5 mm)² = 25 mm²

Find total area of the figure:

• A(total) = A(trapezoid) + A(triangle)
• A(total) = (b₁ + b₂)h/2 + bh/2
• A(total) = (14 + 18)(17 - 12)/2 + 18*12/2 = 80 + 108 = 188

Find the percent value of the ratio of areas of the square and full figure, which determines the probability we are looking for:

• 25/188*100% = 13.2978723404 % ≈ 13.3%

This is matching the choice C.