IMSA Geometry and Spatial Reasoning 2

Question 1

In a right triangle, one leg is 8 and the hypotenuse is 10. What is the other leg?

Accepted Answer

6

Answer

By the Pythagorean theorem: 8² + b² = 10², so 64 + b² = 100, giving b = 6.

Question 2

What is the area of a circle with diameter 12? (Use π ≈ 3.14)

Accepted Answer

113.04

Answer

Radius = 6; Area = πr² = 3.14 × 36 = 113.04.

Question 3

Two parallel lines are cut by a transversal. Alternate interior angles are:

Accepted Answer

Equal

Answer

When a transversal cuts parallel lines, alternate interior angles are always equal.

Question 4

A square has an area of 81 cm². What is its perimeter?

Accepted Answer

36 cm

Answer

Side = √81 = 9 cm; Perimeter = 4 × 9 = 36 cm.

Question 5

What is the measure of each interior angle of a regular pentagon?

Accepted Answer

108°

Answer

Sum of interior angles = (5-2) × 180° = 540°; each angle = 540°/5 = 108°.

IMSA - Intermediate Math Skill Assesment Practice Test