AMC8_Geometry

The midpoints of the four sides of a rectangle are (-3,0), (2,0), (5,4), and (0,4). What is the area of the rectangle?

• 30

• 40

• 12

• 14

Tags

geometry

An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 4, what is the area of the hexagon?

• 8

• 12

• 6

• 7

Tags

geometry

In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller circles have a combined area of 1 square unit, then what is the area of the shaded region, in square units?

• 1

• 4

• 5

• 2

Tags

geometry

From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also a side of the octagon?

• 2/5

• 3/7

• 5/7

• 1/4

Tags

geometry

How many square yards of carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide? (There are 3 feet in a yard.)

• 12

• 31

• 15

• 24

Margie's winning art design is shown. The smallest circle has a radius of 2 inches, with each successive circle's radius increasing by 2 inches. Which of the following is closest to the percent of the design that is black?

• 31

• 38

• 42

• 48

Tags

geometry

Square ABCD has sides of length 3. Segments CM and CN divide the square's area into three equal parts. How long is segment CM?

• √27

• √7

• √13

• √15

Tags

geometry

How many pairs of parallel edges, such as AB and GH or EH and FG, does a cube have?

• 12

• 18

• 19

• 21

Tags

geometry

The figure below shows a polygon ABCDEFGH, consisting of rectangles and right triangles. When cut out and folded on the dotted lines, the polygon forms a triangular prism. Suppose that AH = EF = 8 and GH = 14. What is the volume of the prism?

• 241

• 256

• 192

• 131

Tags

geometry

Isabella uses one-foot cubical blocks to build a rectangular fort that is 12 feet long, 10 feet wide, and 5 feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain?

• 258

• 280

• 121

• 167

Tags

geometry