GMAT Quant: Geometry Formula

Geometry Formula

For any Maths and Quantitative Aptitude sum, formulas are those fundamentals which help you to resonate and solve it. In GMAT Quant, this cheat-sheet list of formulas for Geometry, will assist you in brushing up your basics.

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 \(A = \frac{1}{2} \times b \times h\) 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 \(A = \frac{1}{2} (a + b) \times h\) 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 \(A = \frac{1}{2}r^{2}\theta\) r = Radius
\(\theta\) = angle in radians
Regular n-polygon \(A = \frac{1}{4} \times n \times a^{2} \times \cot \frac{\pi}{n}\)

 

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 = Heightw = 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 \(S = \pi \times r \sqrt{r^{2} + h^{2}}\) 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 = Heightw = 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 \(V = \frac{4}{3} r^{3}\) r  = Radius
Right Circular Cone \(V = \frac{1}{3} \pi r^{2}h\) h = Vertical height
r  = Radius of the base
Square or Rectangular Pyramid \(V = \frac{1}{3} lwh\) l  = Length of the Base
h = Vertical heightw = Width of the Base (In Case of Square, bothe l and w will be equal)

Circle

Circumference of a Circle

\(Circumference \; (C) = \pi d = 2 \pi r\)

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.

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Which 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.

\(a^{2} + b^{2} = c^{2}\)

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