AMC 8 Geometry & Measurement 3

Question 1

A square is inscribed in a circle of radius 5. What is the area of the square?

Accepted Answer

50

Answer

The diagonal of the inscribed square equals the diameter (10), so s√2 = 10, giving s = 5√2 and area = s² = 50.

Question 2

How many lines of symmetry does a regular pentagon have?

Accepted Answer

5

Answer

A regular pentagon has 5 lines of symmetry, one through each vertex and the midpoint of the opposite side.

Question 3

A rectangle's length is three times its width. If the perimeter is 48, what is the area?

Accepted Answer

108

Answer

With l = 3w, the perimeter gives 2(3w + w) = 48, so w = 6, l = 18, and area = 108.

Question 4

In a right triangle, one acute angle is 35°. What is the other acute angle?

Accepted Answer

55°

Answer

The two acute angles in a right triangle are complementary, so the other angle = 90° − 35° = 55°.

Question 5

What is the perimeter of a regular octagon with side length 7?

Accepted Answer

56

Answer

A regular octagon has 8 equal sides, so perimeter = 8 × 7 = 56.

AMC 8 - American Mathematics Competition 8 Practice Test