To solve the geometry questions in the GMAT exam, it’s essential you are thorough with the GMAT Math Geometry formulas as it makes solving questions faster and easier. Here is an article that covers all the essential geometry formulas you need to ace Geometry questions in the GMAT quant section.
So let’s take a look at this GMAT Math Geometry formulas list.
Geometry Questions
Geometry Solutions
Perimeter Formulas
| Shape | Formula | Where, P = Perimeter and |
| Square | P = 4s | s = sides |
| Rectangle | P = 2l + 2w | l = length
w = width |
| Parallelogram | P = 2l + 2w | l = length
w = width |
| Trapezoid or Trapezium | P = s {1} + s {2} + b {1} + b {2} | s {1} and s {2} are two sides and b {1} and b {2} are the two bases of the figure. |
| Triangle | P = s {1} + s {2} + b | s {1} and s {2} are two sides and b = base |
| Rhombus | P = 4l | l = length |
Area Formulas
| Shape | Formula | Where A = Area and |
| Triangle | A = {1} / {2} times b times h | b = base h = vertical height |
| Square | A = a ^ {2} | a = length of side |
| Rectangle | A = w times h | w = width h = height |
| Parallelogram | A = b times h | b = base h = vertical height |
| Trapezoid or Trapezium | A = {1} / {2} (a + b) times h | a, b = length if two sides of the figure h = vertical height |
| Circle | A = pi.r^{2} | r = radius |
| Ellipse | A = pi.ab | a, b = longest and shortest radius of the figure |
| Sector of a Circle | A = {1} / {2} r ^ {2} theta | r = radius theta = angle in radians |
| Regular n-polygon |
A = {1}/{4} times n times a^{2} times cot {pi}/{n}
| n = number of sides a = length of the sides |
Surface Area Formulas
| Shape | Formula | Where S = Surface Area and |
| Rectangular Solid | S = 2lh + 2wh + 2wl | l = length h = height w = width |
| Cube | S = 6s^{2} | s = sides of the cube |
| Right Circular Cylinder | S = 2.pi times rh + 2.pi times r^{2} | h = vertical height of the cylinder r = radius of the base |
| Sphere | S = 4.pi times r^{2} | r = radius |
| Right Circular Cone | S = pi times r^{2} + pi.r times whole root of (r^{2} + h^{2}) | h = vertical height r = radius of the base |
| Torus | S = pi^{2} times (R^{2} – r^{2}) | R = radius of the larger base r = radius of the smaller base |
Volume Formulas
| Shape | Formula | Where V = Volume and |
| Rectangular Solid | V = lwh | l = length h = height w = width |
| Cube | V = s^{3} | s = sides of the cube |
| Right Circular Cylinder | V = pi times r^{2}h | h = vertical height of the cylinder r = radius of the base |
| Sphere | V = {4}/{3} times pi.r^{3} | r = radius |
| Right Circular Cone | V = {1}/{3} pi.r^{2}h | h = vertical height r = radius of the base |
| Square or Rectangular Pyramid | V = {1}/{3} lwh | l = length of the base h = vertical height w = width of the base (In case of square, both l and w will be equal) |
Circle
Circumference of a Circle
Circumference (C) = pi.d = 2 times pi.r
Where, d = Diameter and r = Radius
Area of a Circle
Area (A) = pi.r^{2}
Where, r = Radius
Pythagoras Theorem
The Pythagorean Theorem states that the area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides.
This implies that in the above Triangle, a and b are the lengths of the two legs of the triangle and c is the length of the hypotenuse of the triangle.
a^2 + b^2 = c^2
For any math or quantitative aptitude problem, formulas are those fundamentals that help you to think and solve them with ease. Hence, memorizing these GMAT math geometry formulas thoroughly helps solve easy or even difficult problems faster.
Now that you know these GMAT math Geometry formulas, you’re better positioned to apply these formulas to the various Geometry questions that appear in your practice or mock tests and of course the actual exam.