Perimeter and Surface Area Formulas

Perimeter and surface area formulas are part of the math used in common science calculations. You While it's a good idea to memorize these formulas, here is a list of perimeter, circumference and surface area formulas to use as a handy reference.

01
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Triangle Perimeter and Surface Area Formulas

Triangle
A triangle has three sides. Todd Helmenstine

A triangle is a three-sided closed figure.
The perpendicular distance from the base to the opposite highest point is called the height ( h ).

Perimeter = a + b + c
Area = ½bh

02
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Square Perimeter and Surface Area Formulas

Square
Squares are four-sided figures where each side is of equal length. Todd Helmenstine

A square is a quadrangle where all four sides are of equal length.

Perimeter = 4s
Area = s2

03
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Rectangle Perimeter and Surface Area Formulas

Rectangle
A rectangle is a four-sided figure with all interior angles are right angles and opposing sides have equal lengths. Todd Helmenstine

A rectangle is a special type of quadrangle where all the interior angles are equal to 90° and all opposite sides are the same length.
The perimeter ( P ) is the distance around the outside of the rectangle.

P = 2h + 2w
Area = h x w

04
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Parallelogram Perimeter and Surface Area Formulas

Parallelogram
A parallelogram is a quadrangle where opposite sides are parallel to each other. Todd Helmenstine

A parallelogram is a quadrangle where opposite sides are parallel to each other.
The perimeter ( P ) is the distance around the outside of the parallelogram.

P = 2a + 2b

The height ( h ) is the perpendicular distance from one parallel side to its opposite side.​

Area = b x h

It is important to measure the correct side in this calculation. In the figure, the height is measured from side b to the opposite side b, so the Area is calculated as b x h, not a x h. If the height was measured from a to a, then the Area would be a x h. Convention considers the side the height is perpendicular to is called the 'base' and usually denoted with a b.

05
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Trapezoid Perimeter and Surface Area Formulas

Trapezoid
A trapezoid is a quadrangle where only two opposing sides are parallel to each other. Todd Helmenstine

A trapezoid is another special quadrangle where only two sides are parallel to each other.
The perpendicular distance between the two parallel sides is called the height ( h ).

Perimeter = a + b1 + b2 + c
Area = ½( b1 + b2 ) x h

06
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Circle Perimeter and Surface Area Formulas

Circle
A circle is a path where the distance from a center point is constant. Todd Helmenstine

A circle is an ellipse where the distance from the center to the edge is constant.
Circumference ( c ) is the distance around the outside of the circle.
Diameter ( d ) is the distance of the line through the center of the circle from edge to edge.
Radius ( r ) is the distance from the center of the circle to the edge.
The ratio between the circumference and the diameter is equal to the number π.​

d = 2r
c = πd = 2πr
Area = πr2

07
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Ellipse Perimeter and Surface Area Formulas

Ellipse
An ellipse is a figure outlined by a path where the sum of the distances from two focal points are constant. Todd Helmenstine

An ellipse or oval is a figure that is traced out where the sum of the distances between two fixed points is a constant.
The shortest distance between the center of an ellipse to the edge is called the semiminor axis ( r1 )
The longest distance between the center of an ellipse to the edge is called the semimajor axis ( r2 )

Area = πr1r2

08
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Hexagon Perimeter and Surface Area Formulas

Hexagon
A regular hexagon is a six sided polygon where each side is of equal length. Todd Helmenstine

A regular hexagon is a six-sided polygon where each side is of equal length. This length is also equal to the radius ( r ) of the hexagon.

Perimeter = 6r
Area = (3√3/2 )r2

09
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Octagon Perimeter and Surface Area Formulas

Octagon
A regular octagon is a eight sided polygon where each side is of equal length. Todd Helmenstine

A regular octagon is an eight-sided polygon where each side is of equal length.

Perimeter = 8a
Area = ( 2 + 2√2 )a2