geometry formula

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. 

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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. 

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