All GMAT Math Resources
Example Questions
Example Question #31 : Polygons
What is the median of the measures of the angles of a nonagon (a nine-sided polygon)?
The question cannot be answered without knowing the measures of the individual angles.
The question cannot be answered without knowing the measures of the individual angles.
The sum of the measures of the nine angles of any nonagon is calculated as follows:
The median of an odd quantity of numbers is the number that falls in the center position when they are arranged in ascending order; for nine numbers, it will be the fifth-highest number. We now need to show that we need to know the actual numbers in order to find the median.
Case 1: Each angle measures .
The set is and the median is 140.
Case 2: Eight of the angles measure and one of them measures .
The set is and the median is 139.
In both cases, the sum of the angle measures is 1,260, but the medians differ between the two.
Example Question #701 : Gmat Quantitative Reasoning
Note: Figure NOT drawn to scale.
Given Regular Pentagon . What is ?
Quadrilateral is a trapezoid, so .
, so
Example Question #461 : Geometry
The angles of a pentagon measure .
Evaluate .
This pentagon cannot exist
The sum of the degree measures of the angles of a (five-sided) pentagon is , so we can set up and solve the equation:
Example Question #702 : Gmat Quantitative Reasoning
The measures of the angles of a pentagon are:
What is equal to?
The degree measures of the interior angles of a pentagon total , so
Example Question #703 : Gmat Quantitative Reasoning
What is the measure of an angle in a regular octagon?
On octagon has sides. The word regular means that all of the angles are equal. Therefore, we can use the general equation for finding the angle measurement of a regular polygon:
, where is the number of sides of the polygon.
.
Example Question #31 : Polygons
What is the measure of one exterior angle of a regular twenty-four sided polygon?
The sum of the measures of the exterior angles of any polygon, one at each vertex, is . Since a regular polygon with twenty-four sides has twenty-four congruent angles, and therefore, congruent exterior angles, just divide:
Example Question #34 : Polygons
A pentagon with a perimeter of one mile has three congruent sides; one of the other sides is 100 feet longer than any of those three congruent sides, and the remaining side is 100 feet longer than that fourth side. What is the length of that longest side?
If each of the five congruent sides has measure , then the other two sides have measures and . Add the sides to get the perimeter, which is equal to 5,280 feet, the solve for :
Each of the shortest sides is 996 feet long; the longest side is feet long.
Example Question #1 : Calculating The Length Of A Side Of A Polygon
The perimeter of a regular hexagon is one-half of a mile. Give the sidelength in inches.
One mile is 5,280 feet. The perimeter of the hexagon is one-half of this, or 2,640 feet. Since each side of a regular hexagon is congruent, the length of one side is one-sixth of this, or feet.
Multiply by 12 to convert to inches: inches.
Example Question #711 : Problem Solving Questions
The perimeter of a regular pentagon is one-fifth of a mile. Give its sidelength in feet.
One mile is 5,280 feet. The perimeter of the pentagon is one-fifth of this, or feet. Since each side of a regular pentagon is congruent, the length of one side is one fifth-of this, or feet.
Example Question #1 : Calculating The Length Of A Side Of A Polygon
The perimeter of a regular octagon is two kilometers. Give its sidelength in meters.
One kilometer is equal to 1,000 meters, so two kilometers comprise 2,000 meters. A regular octagon has eight sides of equal length, so divide by 8 to get the sidelength: meters.