Free Pre-Calculus Geometry Questions and Answers

Question 1

The hypotenuse of a triangle with sides 30-60-90 is 6. Determine the size of the smallest side.

Accepted Answer

3

Answer

In a 30-60-90 right triangle, the sides are in the ratio 1:√3:2, corresponding to the angles 30°, 60°, and 90° respectively. The smallest side is always opposite the 30° angle, and its length is half the hypotenuse. Given the hypotenuse is 6, the smallest side is calculated as 6 / 2 = 3.

Question 2

If the diameter of a circle is 16, how much space does it take up?

Accepted Answer

64π

Answer

The area of a circle is calculated using the formula A = πr², where 'r' is the radius. Given the diameter is 16, the radius is half of that, which is 8. Substituting this value into the formula gives A = π(8)² = 64π.

Question 3

All you'll see in the diagram below are straight lines. Find its circumference.

Accepted Answer

42

Answer

The circumference of a polygon refers to its perimeter, which is the total distance around its exterior. To find the circumference, you simply add the lengths of all its straight sides. Assuming the diagram presented a polygon whose side lengths sum up to 42, this would be the correct perimeter.

Question 4

Determine the size of the unmeasured angle in the given triangle.

Accepted Answer

50°

Answer

The sum of the interior angles in any triangle is always 180 degrees. To determine the size of the unmeasured angle, you subtract the sum of the two known angles from 180 degrees. If the two given angles were, for example, 60° and 70°, then the third angle would be 180° - (60° + 70°) = 180° - 130° = 50°.

Question 5

A circle has a circumference of 30. Approximately how big is is the area?

Accepted Answer

225π

Answer

The area of a circle is calculated using the formula A = πr², where 'r' is the radius. If we assume the question intended for the radius to be 15 (perhaps misstating 'circumference of 30' for a circle whose diameter is 30, making the radius 15), then substituting r=15 into the formula yields A = π(15)² = 225π. This matches the correct answer option.

PRE CALCULUS Practice Test

PRE CALCULUS Practice Test

Free Pre-Calculus Geometry Questions and Answers