Completing an entire worksheet on a single subject is one thing, but having to know a half-dozen formulas and the right shape to use them all on is something entirely different. The worksheets on this page will give you practice calculating perimeter and area for various shapes. Here are a few things to remember before you get started:

1. Perimeter is the Path around an object. If one of the shapes has a distance labeled that goes through the center of the shape, don’t use that number when calculating the perimeter. You will only use the lengths of the sides that make up the outside of the shape.
2. Because perimeter represents a distance, it’s always labeled in units (i.e. miles, inches, centimeters).
3. Area is the space inside of a shape. Think of what it would look like if you covered a shape with a blanket and cut off anything that hung over the sides. That’s area.
4. Area is always labeled in square units (i.e. square miles, square inches, square centimeters).

Here are some practice problems to help in case you get stuck:

1.) Find the perimeter and area of the following rectangle.

PERIMETER:
The formula for the perimeter of a rectangle is:
P = 2ℓ + 2w where ‘ℓ’ is the length and ‘w’ is the width.
P = 2(3 in) + 2(5 in)
P = 6 in + 10 in
P = 16 in.

AREA:
The formula for the area of a rectangle is:
A = ℓw or length times width.
A = (3 in)(5 in)
A = 15 in²

2.) Find the perimeter and area of the following triangle.

PERIMETER:
Perimeter is always the path around the object.
All you need to do is add the lengths of the 3 sides (lengths are in black text).
P = 22 cm + 15 cm + 26 cm
P = 63 cm

AREA:
The formula for the area of a triangle is:
A = ½ b • h
A = ½(26 cm)(10 cm)
A = (13 cm)(10 cm)
A = 130 cm²

3.) Find the perimeter and area of the following parallelogram:

PERIMETER:
All we need here are the length of the base (10 in) and the slant height (7.5 in).
Since a parallelogram has two sets of parallel sides, we know that opposite sides will be the same length.
To find the perimeter add 10 in + 7.5 in + 10 in + 7.5 in.
Perimeter = 35 in.

AREA:
The formula for the area of a parallelogram is:
A = b • h
A = (10 in)(7 in)
A = 70 in²

4.) Find the perimeter and area of the following trapezoid:

PERIMETER:
To find the perimeter, add the lengths of the four sides.
Perimeter =  15 in + 8.5 in + 12 in + 8.5 in
Perimeter = 44 in

AREA:
The only numbers we need from our picture are base one (15 in), base two (12 in), and the height (8 in).
Area = ½(b_₁+b_₂)h
A = ½(15 in + 12 in)(8 in)
A = ½(27 in)(8 in)
A = (13.5 in)(8 in)
A = 108 in²

5.) Find the perimeter and area of the following composite shape:

First, divide the larger figure into smaller shapes. (There are frequently multiple ways of doing this step, but for the case of our example we’ll divide it into one square and one rectangle.) Then, use the information you know to add in the missing side lengths.

PERIMETER:
Perimeter is always the path around the object.
Now that you know all of the side lengths, just add them together to find the perimeter.
P = 10 in + 10 in + 5 in + 5 in + 5 in + 5 in
P = 40 in.

AREA:
Area is the space inside. To find the area of the composite shape, find the area of the square and the rectangle individually. Then, add them together.

Area of this composite shape = Area of the square + Area of the rectangle.
Area = 25 in² + 50 in²
Area = 75 in²