IMSA Geometry and Spatial Reasoning 3

Question 1

What is the length of the diagonal of a square with side length 6?

Accepted Answer

6√2

Answer

By the Pythagorean theorem: diagonal = √(6² + 6²) = √72 = 6√2.

Question 2

Angles in a triangle measure x, 2x, and 3x. What is the value of x?

Accepted Answer

30°

Answer

x + 2x + 3x = 180°, so 6x = 180°, giving x = 30°.

Question 3

What is the surface area of a cube with side length 4?

Accepted Answer

96

Answer

A cube has 6 faces, each with area 4² = 16, so surface area = 6 × 16 = 96.

Question 4

Which set of side lengths can form a right triangle?

Accepted Answer

5, 12, 13

Answer

5² + 12² = 25 + 144 = 169 = 13², confirming it satisfies the Pythagorean theorem.

Question 5

Two angles are complementary. One measures 34°. What is the other?

Accepted Answer

56°

Answer

Complementary angles sum to 90°, so the other angle is 90° - 34° = 56°.

IMSA - Intermediate Math Skill Assesment Practice Test