The perimeter of a 2D shape, such as square, rectangle or triangle, is the sum of all the sides of the shape.
For a circle, the perimeter is the length of the boundary of the circle called the circumference..

## Perimeter of Common Shapes

Let's look at how to calculate the perimeter of the shapes below:

### Triangle

The perimeter of a triangle is calculated by:

\(P = a + b + c\)

### Square

The perimeter of a square with length s is calculated by:

\(P = 4s\)

### Rectangle

The perimeter of a rectangle with sides l and h is calculated by:

\(P = 2*l + 2*w\)

### Circle

The perimeter of a circle with radius r is calculated by:

\(P = 2 \pi r\)

### Trapezoid

The perimeter of a trapezoid with side lengths a, b, c and dis calculated by:

\(P = a + b + c + d\)

### Parallelogram

The perimeter of a parallelogram with side lengthsl and w is calculated by:

\(P = 2 \cdot a + 2 \cdot b\)

An isosceles triangle has a perimeter of \(44 \) m. The base is \(10\) m long. What is the length of the other sides?

Show Answer
An isosceles triangle has two equal lengths. The other length is known.

Using the formula for the perimeter we can write:

\(P = a + b + c \)

Since two sides are the same, we can change one c to a b:

\(P = a + b + b \)

Plug in what we know:

\(44 = 10 + 2b\)

Finally, solve for b:

\(b = 17\) m

The other sides are both \(17 \) m.

Find the perimeter of the semi-circle below:

Show Answer
The perimeter of the semi-circle is half the perimeter of the full circle plus the diameter:

\(P = \cfrac{1}{2} 2\pi r + 2r \)

The diameter is given so the radius can be calculated as:

\(r = \cfrac{d}{2} = \cfrac{43}{2} = 21.5\)

Plug in the radius and solve:

\(P = \cfrac{1}{2} 2\pi (21.5) + 2(21.5) \)

\(P = 110.54 \; \) cm

The perimeter is \(110.54\) cm.

An analog clock with a radius of 20 cm is being observed.
The second hand, with its arrows touching the outer edge of the clock, spun 3 full rotations (3 min).
What's the total distance the second hand's arrow travelled?

Show Answer
First we need to find the perimeter of the clock using the formula of a circle::

\(P = 2 \pi r\)

\(P = 2 \pi (20) \)

\(P = 125.6\) cm

Because the second hand spun 3 times, it travels 3 times the perimeter:

\(125.6 \cdot 3 = 376.8\) cm

The second hand travelled 376.8 cm in total during 3 full rotations around the clock.