AST Geometry and Trigonometry

Question 1

What is the area of a circle with radius 6?

Accepted Answer

36π

Answer

The area of a circle is πr², so π(6)² = 36π.

Question 2

What is the sum of the interior angles of a pentagon?

Accepted Answer

540°

Answer

The sum of interior angles of an n-sided polygon is (n−2)×180°, so (5−2)×180° = 540°.

Question 3

A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?

Accepted Answer

5

Answer

By the Pythagorean theorem, c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Question 4

What is the area of a triangle with base 10 and height 6?

Accepted Answer

30

Answer

The area of a triangle is ½ × base × height = ½ × 10 × 6 = 30.

Question 5

Two parallel lines are cut by a transversal. Which pair of angles is supplementary?

Accepted Answer

Co-interior (same-side interior) angles

Answer

Co-interior (same-side interior) angles add up to 180° when formed by parallel lines and a transversal.

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