Perimeter, perimeter formulas

A perimeter of a figure is the sum of the lengths of all sides.

The standard notation for perimeter in math is P

Perimeter of a triangle


P = a + b + c

Perimeter of a square


Squares have four equal sides.
Let the length of side be a.
The perimeter of а square is P = a + a + a + a or:

P = 4 ⋅ a

Perimeter of a rectangle


Let the length and width of a rectangle be a and b.
The sum of the lengths of the sides is P = a + b + a + b or:

P = 2 ⋅ a + 2 ⋅ b

Perimeter of a parallelogram


Since the opposite sides of a palallelogram are equal in length its perimeter is P = a + b + a + b or:

P = 2 ⋅ a + 2 ⋅ b

As we see the perimeter of the parallelogram is equal the perimeter of the rectangle.

Perimeter of a rhombus

P = 4 ⋅ a

Perimeter of an isosceles trapezoid


Let a and b be the lengths of the parallel sides. Since it is isosceles the other two sides are equal in length and let c be their length.

P = a + b + c + c = a + b + 2 ⋅ c

Perimeter of an equilateral triangle

equilateral triangle

As we know equilateral triangles have 3 equal sides. So if the length of a side is a then the perimeter formula is P = a + a + a

P = 3 ⋅ a

Circumference of a circle


$C = d \cdot \pi = 2 \cdot r \cdot \pi$

$\pi = 3.14$
r is radius.
d is diameter.

Regular polygon

Perimeter of regular polygon

$P = 2nb\sin\frac{\pi}{n}$

n is the number of edges(vertices).
$\pi = 3.14159265359$

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