AMC 8 Geometry & Measurement 2

Question 1

What is the volume of a rectangular box with dimensions 3 × 4 × 5?

Accepted Answer

60

Answer

Volume = length × width × height = 3 × 4 × 5 = 60 cubic units.

Question 2

In a right triangle, the two legs are 5 and 12. What is the length of the hypotenuse?

Accepted Answer

13

Answer

By the Pythagorean theorem, hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13.

Question 3

A trapezoid has parallel bases of length 6 and 10, and a height of 4. What is its area?

Accepted Answer

32

Answer

Area = ½ × (b₁ + b₂) × h = ½ × (6 + 10) × 4 = 32.

Question 4

Two supplementary angles are in the ratio 2:7. What is the measure of the larger angle?

Accepted Answer

140°

Answer

Let the angles be 2x and 7x; then 2x + 7x = 180°, giving x = 20°, so the larger angle = 7 × 20° = 140°.

Question 5

How many degrees are there in the sum of the interior angles of a pentagon?

Accepted Answer

540°

Answer

The interior angle sum of a pentagon = (5−2) × 180° = 3 × 180° = 540°.

AMC 8 - American Mathematics Competition 8 Practice Test