Perimeter and Area

Perimeter and Area

For each shape, you can find the perimeter and area.


Perimeter is just the distance around the outside of the shape and the area is the amount of space the shape takes up.


Different shapes have different ays to find the perimeter and area. This chart shows the formulas for a few basic shapes.


Let’s look at each shape and learn more about its area and perimeter.

Circles

Symbols

    • π (pi) is just a special number almost equal to 3.14 and used for a circle’s area and perimeter

    • r is the radius of the circle as shown in the picture

    • d is the diameter of the circle and is double the radius

Area

    • The area of a circle is found by squaring the radius (multiplying radius x radius) and multiplying that by π

Perimeter

    • The perimeter of a circle can be found by multiplying 2 times the radius times π

    • This is also the same as multiplying the diameter times π

Parallelogram

Symbols

    • b is the base, or bottom of the parallelogram

    • h is the height or the distance from the top straight to the bottom (straight line)

    • s is the slanted sides of the shape

Area

    • The area is found by multiplying the base and height

Perimeter

    • The perimeter is just adding all four sides of the shape, or two times the base plus two times the sides

Rectangle

Symbols

    • l is the length (long side)

    • w is the width (short side)

Area

    • The area is found by multiplying the length and width

Perimeter

    • The perimeter is just adding all four sides of the shape, or two times the width plus two times the length

Rhombus

Symbols

    • d1 and d2 are the diagonals of a rhombus

    • s is the side of a rhombus (same for all four equal sides)

Area

    • The area is multiplying the diagonals and dividing the result by 2

Perimeter

    • The perimeter is adding all four sides, or 4 times s

Square

Symbols

    • s is the side of a square (same for all four equal sides are equal)

Area

    • The area is squaring the side length (side x side)

Perimeter

    • The perimeter is adding all four sides, or 4 times s

Trapezoid

Symbols

    • b1 and b2 are the bases of a trapezoid

    • h is the height of the trapezoid

    • s1 and s2 are the other two sides of a trapezoid

Area

    • The area is adding the bases together, dividing that result by two, and multiplying it by the height

Perimeter

    • The perimeter is found by adding all four sides together (bases plus two other sides)

Triangle

Symbols

    • b represents the base of a triangle

    • h represents the height of a triangle

    • s represents all the side lengths

Area

    • The area is found by multiplying the base and height and dividing that result by 2

Perimeter

    • The perimeter is all the sides added together

Example 1. Find the area and perimeter of the triangle on the right:

Area: the area of a rectangle is the length times width. The length in this example is 7 and the width is 4. So the area would be:

4 x 7 = 28 in.


Perimeter: the perimeter is adding all of the sides together, or length plus width times 2. So the perimeter would be:

(4 + 7) x 2 = 11 x 2 = 22 in.

Example 2. Find the area and perimeter of the triangle on the right:

The area of this triangle is the height times base divided by 2. The height is 7 and the base is 24. So the area would be:

(7 x 24) / 2 = 168 / 2 = 84 in.


The perimeter of this triangle is all the sides added together. So the perimeter would be:

7 + 24 + 25 = 56 in.

Memorizing these formulas is important because they are the basic formulas that you can see in many problems. Here are some links you can use to get more practice or learn the formulas again.

Take this quiz to test your knowledge of shapes’ area and perimeter!



Note: If a redirection notice appears, click on the link shown to access the quiz.