Area Formulas and Perimeter Formulas

Area formulas and perimeter formulas are formulas that pop up often in different homework problems. Examples include problems involving pressure, mechanical torque and electric resistance. You could just memorize these formulas, but why do that when this handy reference is available?

Triangle Area Formula and Triangle Perimeter Formula

TriangleA triangle is a figure formed by three connected sides. The perimeter is the sum of the lengths of the sides. The ‘height’ (h) of a triangle is the highest point opposite of the side you choose as the base.

Perimeter of a Triangle = a + b + c

Area of a Triangle = ½b · h

Parallelogram Area Formula and Parallelogram Perimeter Formula

ParallelogramA parallelogram is a closed figure formed by four sides and the opposite sides are parallel to each other. The ‘height’ (h) of a parallelogram is the distance from the measured side to its opposite parallel side.

Perimeter of a Parallelogram = 2a + 2b

Area of a Parallelogram = b ⋅ h

Rectangle Area Formula and Rectangle Perimeter Formula

A rectangle is a special parallelogram where the interior angles are all right angles.

Perimeter of a Rectangle = 2H + 2W

Area of a Rectangle = H · W

Square Area Formula and Square Perimeter Formula

A square is a special type of rectangle composed of four equal length sides.

Perimeter of a Square = 4s

Area of a Square = s2

Trapezoid Area Formula and Trapezoid Perimeter Formula

A trapezoid is another special quadrilateral (four-sided figure) where two of the sides are parallel. The ‘height’ (h) of a trapezoid is the distance between the two parallel sides.

Perimeter of a Trapezoid = a + b1 + b2 + c

Area of a Trapezoid = ½(b1 + b2) · h

Ellipse Area Formula and Ellipse Perimeter Formula

EllipseAn ellipse is a closed figure where the path traced when the sum of the distances between two fixed points is a constant. The semiminor axis of the oval is the shortest distance from the center of the ellipse (r1) and the semimajor axis (r2) is the longest distance from the center.

Perimeter of an Ellipse

It’s actually not an easy thing to calculate the perimeter of an ellipse. If the semimajor and semiminor axes are about the same size (within 3x the length of each other), the perimeter can be approximated using the formula:

Ellipse Perimeter Approximation #1

A closer approximation can be determined using this expression:

The ‘exact’ solution can be calculated using an infinite series. First, you’ll need to calculate the eccentricity of the ellipse using the formula

eccentricity formular

Then use this value in the expression

Ellipse Perimeter Infinite Series

While the perimeter formula is complicated, the area formula is straightforward.

Area of an ellipse = πr1r2

Circle Area Formula and Circle Perimeter Formula

A circle is a special ellipse where the semimajor and semiminor axes are the same size. All the points are the same distance from the center. This distance is known as the radius. The distance across the widest point of a circle is known as the diameter.

The perimeter of a circle is also known as the circumference.

Perimeter of a Circle = 2πr = πd

Area of a Circle = πr2

Hexagon Area Formula and Hexagon Perimeter Formula

A regular hexagon is a six-sided figure where each of the sides is of equal length. The length of these sides is equal to the distance from the center to the widest point of the hexagon.

Perimeter of a Hexagon = 6r

Area of a Hexagon = (3√3)/2 ⋅ r2

Octagon Area Formula and Octagon Perimeter Formula

OctagonA regular octagon is an eight-sided figure with equal length sides.

Perimeter of an Octagon = 8a

Area of an Octagon = (2 + 2√2)a2