List of top Quantitative Aptitude Questions on Geometry asked in GRE

What is the equation of the new parabola created by shifting \( y = x^2 \), three units in the positive y-axis direction?
A sphere with diameter 1 unit is enclosed in a cube of side 1 unit each. Find the unoccupied volume remaining inside the cube.
The function \( y = -3x^2 \) is shifted 2 units towards the positive x-axis (right) and 3 units towards the positive y-axis (up). Find the resulting function.
Find the shaded area when two squares with side \( a \) intersect as shown in the figure below.
If the largest side of a triangle is \( A \), and the other two sides are \( B \) and \( C \), what relation exists between them?
What is the area of triangle ALC in the figure given below?
The width of a rectangle is \( \frac{2}{3} \) times its length. If the length is calculated to be 9, what is the value of the perimeter for this rectangle?
Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices: R is the center of the circle below: Figure NOT drawn to scale Quantity A: Half the circumference
Quantity B: The area of triangle QRS
Lines \( l \) and \( m \) are parallel. \( O \) is the center of the circle. The measure of angle \( d \) is \( 45^\circ \). The length of line \( RS \) is \( \frac{\sqrt{2}}{2} \). Line \( RS \) forms a right angle with line \( m \). What is the measure of angle \( a \)?
Lines \( l \) and \( m \) are parallel. \( O \) is the center of the circle. The measure of angle \( d \) is \( 45^\circ \). The length of line \( RS \) is \( \frac{\sqrt{2}}{2} \). Line \( RS \) forms a right angle with line \( m \). What is the length of line PR?
Lines \( l \) and \( m \) are parallel. \( O \) is the center of the circle. The measure of angle \( d \) is \( 45^\circ \). The length of line \( RS \) is \( \frac{\sqrt{2}}{2} \). Line \( RS \) forms a right angle with line \( m \). What is the diameter of circle O?
Rectangle R has length 30 and width 10, and square S has length 5. The perimeter of S is what fraction of the perimeter of R?
For a project, a square piece of cloth is folded in half and sewed together to form a rectangle that has a perimeter of 36 centimeters. What was the area in square centimeters of the piece of cloth before it was folded?
If the vertices of a triangle have rectangular coordinates \((0,0)\), \((8,0)\), and
\((8,6)\), respectively, then the perimeter of the triangle is
In the figure above, \( x = \)
In the figure above, if PQRS is a parallelogram, then \( x = \)
If (7, 3) is the center of the circle above, then the radius of the circle could be equal to which of the following?

If each shaded circular region in the figure above has radius 5, then the total area of the shaded regions is what fraction of the area of the square region? 

 

In the figure above, ABCE is a square. What are the coordinates of point B? 

 

Which of the following points (x, y) is NOT on the graph of \(y<2x\)?
The figure above shows a semicircle with center O and a quarter circle with center R. If OQ = 4 and QR = 6, what is the ratio of the area of the shaded region to the area of the semicircular region?


COLUMN A: The perimeter of the shaded region in the rectangle
COLUMN B: \(2\sqrt{2}+2\)

A rectangular parking lot 2x feet long and x feet wide is to be enlarged so that the lot will be 2 times as long and 3 times as wide as it is now. The area of the enlarged rectangular lot will be how many times the area of the present lot?


COLUMN A: The length of ST
COLUMN B: The length of RS


The figure shows a cube with edge of length e.
COLUMN A: The length of diagonal AB
COLUMN B: \(\sqrt{2}e\)