Perimeter, perimeter formulas

Perimeter of a figure is the sum of the lengths of all sides.

Not all figures have perimeter, for example a ball(sphere) does not have a perimeter.

The standard notation for perimeter in math is the letter P


Perimeter of a square

square

Let's a square side is long a. Square have four equal sides so square perimeter is P = a + a + a +a or:

P = 4a

Perimeter of a rectangle

rectangle

Let's a rectangle sides are long a and b.
The length of all its sides is P = a + b + a + b or:

P = 2a + 2b

Perimeter of a parallelogram

parallelogram

Let's palallelogram sides are long a and b
The length of all its sides is P = a + b + a + b so parallelogram perimeter is:

P = 2a + 2b

As you can see the perimeter of the parallelogram is equal the perimeter of the rectangle.

Perimeter of an isosceles trapezoid

trapezoid

Say the length of the parallel sides of a trapezoid are long a and b and the other two sides are long c(As we know isosceles trapezoid has two equal sides).

P = a + b + c + c = a + b + 2c

Perimeter of an equilateral triangle

equilateral triangle

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

P = 3a

Perimeter of a parallelepiped

rectangular parallelepiped

Parallelepiped is a figure that all sides are parallelogram.(Rectangular parallelepipeds is a figure that sides are rectangles.)
If bottom edges are long a and b then the perimeter of the bottom is P = 2a + 2b. Every parallelepiped have two bottoms so the perimeter of the two bottoms is (2a + 2b).2 = 4a + 4b. As we know parameter is sum of all edges. So we have to add four times c

P = 4a + 4b + 4c

Perimeter of a cube

cube

Cube is a parallepiped that sides are squares(all edges are equal).
So the perimeter of a cube is the number of edges * length.
Every cube has 12 edges.
So the perimeter formula of a cube is:

P = 12a
where a is the edge length.

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