High School: Geometry

Directions: What is the side length of an equilateral triangle that has an area of 5 square units? Source: Robert Kaplinsky

Directions: How many squares are shown in the diagram below? Source:  This problem was found in the Fifth Edition Elementary Geometry for College Students by Alexander and Koeberlein

Directions: How many points with two integer coordinates are 5 units away from (-2, 3)? Source: Dylan Kane

Directions: A cone is twice as tall as a cylinder of the same radius. What is the ratio of their volumes? Source: Dylan Kane

Directions: Using any integers, fill in the blanks to Fill in the blanks with integers so that: The equation’s graph is a circle. The circle has the biggest area The circle is completely inside the first quadrant The circle’s radius is a whole number 1 through 9. Source: Nanette Johnson

Directions: What is the longest chord in a circle that has an area of 25π square units? Source: Nanette Johnson

Directions: Using the digits 1 to 9 as many times as you want, fill in the boxes to make the biggest circle: Source: Robert Kaplinsky

Directions: Which circle is bigger?  Circle A with an area of 25 square units or Circle B with the equation x^2 + y^2 = 25 Source: Robert Kaplinsky

Directions: What is the least number of geometric markings to show that a quadrilateral is a kite? Source: Nanette Johnson

Directions: What is the least number of geometric markings needed to demonstrate that a quadrilateral is a square? Source: A collaborative effort of Jose De La Torre and Nanette Johnson answer by Ricardo Navarro with help from Robert Kaplinsky