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GRE Geometry Practice Questions
Free GRE Quantitative practice questions on geometry. Ten audit-passed questions with full explanations, covering triangles, circles, polygons, lines, angles, and coordinate geometry from easy to hard difficulty.
More questions
A pentagon is formed by attaching a right triangle to a rectangle as shown. The rectangle has length 8 and width 6. The right triangle has one leg of length 6 (aligned with the rectangle's width) and hypotenuse of length 10. What is the total area of the pentagon?
A rectangular garden has a perimeter of 28 meters and a diagonal of 10 meters. What is the area of the garden in square meters?
A regular polygon has interior angles measuring 150 degrees each. One of its sides forms the hypotenuse of a right triangle with legs measuring 3 units and 4 units. What is the perimeter of the polygon?
A regular octagon has a perimeter of 32 units. If the octagon is divided into 8 congruent isosceles triangles by drawing lines from the center to each vertex, what is the length of one side of the octagon?
A pentagon has sides of lengths 5, 5, 12, 12, and 12. If one of the angles between the sides of length 5 and 12 is a right angle, what is the sum of the interior angles of the pentagon?
Hard questions
A software company's subscription sales are divided among Basic, Pro, and Premium plans in the ratio 1:2:3. When represented on a pie chart, each plan's sales correspond to a sector with central angle proportional to its sales share. If the pie chart has radius 6 units, what is the arc length of the Premium sector? (Note: Arc length is calculated using radians.)
A circular pizza with radius 6 inches is cut into 8 equal slices. What is the area, in square inches, of one slice?
Two concentric circles have radii of 4 and 6. A sector with a central angle of 30 degrees is drawn in each circle, bounded by the same two radii. What is the ratio of the area of the smaller sector to the arc length of the larger sector?
Quantity A: The area of an equilateral triangle with side length where is the smallest integer for which the area exceeds 100 Quantity B: The area of a regular hexagon with side length
Note: Both shapes are regular polygons.
Quantity A: The area of a circular sector with central angle 60 degrees cut from a circle of radius 10 Quantity B: The area of a circle with diameter equal to the length of the arc bounding the sector in Quantity A
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