Perimeter and Area

Please view this tutorial and answer the follow-up questions on loose leaf to

turn in to your teacher.

Definitions

• Perimeter: The distance around the outside of a plane shape

• Circumference: The distance around the outside of a circle

• Area: The amount of space taken up by a plane shape

Perimeter

When you are finding the perimeter of a plane

shape, you must add up the lengths of each side

of the shape.

12 ft

16 ft

12 ft

16 ft

Pick a starting point and then continue to work your way around the shape until all sides have

been accounted for.

Perimeter

I’ll choose the top left corner as my starting

point.

12 ft

16 ft

12 ft

16 ft

1212 +1612 +16 +1212 +16 +12 +1612 +16 +12 +16 =56

Perimeter

So the perimeter of this rectangle is 56 ft.

12 ft

16 ft

12 ft

16 ft

1212 +1612 +16 +1212 +16 +12 +1612 +16 +12 +16 =56

PerimeterThe perimeter of a circle is called the

circumference.

To find the circumference of a circle, you can use the following formulas:

C =2πr C =πdor

Let’s take a look at an example.

Perimeter

5 ft

C =2πr C =πdor

5 is the radius so we can use the first formula.

Do we have the radius or the diameter?

Perimeter

5 ft

C =2πr C =πdor

Let’s use 3.14 for pi and 5 for the radius.

C =2(3.14)(5)C =31.4 ft

Triangle: Circle:

Rectangle: Square:

Parallelogram:

Trapezoid:

AreaThe following is a list of formulas for basic plane

shapes:

A =lw

A =bh

A =s2

A =πr2A =

12bh

A =12(b1 +b2 )h

Area

5 ft

First, let’s try to find the area of a triangle.

6 ft

4 ft

A =12bh

We can always tell which values are the

base and height because they will

always meet at a right angle.

Area

5 ft

First, let’s try to find the area of a triangle.

6 ft

4 ft

A =12bh

In this case, 6 ft is the base of the triangle and

4 ft is the height.

A =12(6)(4)

A =12 ft2

Area

8 ft

Next up…a rectangle!

10 ft

10 is the length and 8 is the width. Plug

these values into the formula to find the

area.

A=80 ft2

A =lwA =(10)(8)

Area

4 ft

You can use the same formula to find the area of a square.

4 ft A=16 ft2

A =lwA =(4)(4)

Area

4 ft

Or you can use the formula for a square.

4 ft A =16 ft2

A =lwA =(4)(4)

A =s2

A =42

A=16 ft2You’ll get the same

answer for both.

Area

11 m

Parallelograms are similar to rectangles, but you have to be careful to choose the correct values from the figure. You’ll need to find a base and

height.

7 m

Which values would you choose for the base and height?

5 m

Area

11 m

Since we know that base and height always meet at a right angle, we should choose 11 for

our base and 5 for our height.

7 m5 m

A =bh

A =(11)(5)

A =55m2

Area

21 in

For a trapezoid, you’ll need to find two bases and a height. Look for two sides that are parallel

and the length that connects them.

14 in

9 inWhich two sides are

parallel?

Area

21 in

The sides with lengths of 14 in. and 21 in. are parallel. They are connected by a height of 9 in.

14 in

9 in Plug these values into the formula to find the area of this

trapezoid.

A =12(b1 +b2 )h

Area

21 in

The sides with lengths of 14 in and 21 in are parallel to each other. They are connected by a

height of 9 in.

14 in

9 in

A =12(b1 +b2 )h

A =12(21+14)(9)

A =157.5in2

AreaTo find the area of a circle, you’ll need to find

the radius of that circle.

6 cm

What is the value of the radius in this

circle?

Since 6 is the diameter, we need to divide it by 2

to find the radius.

AreaTo find the area of a circle, you’ll need to find

the radius of that circle.

6 cm

So, the radius is 3.

Plug this value into the formula to find the area

for this circle.

AreaTo find the area of a circle, you’ll need to find

the radius of that circle.

6 cm

HINT: Use 3.14 for π.

A=πr2

A =3.14(32 )

A =28.26cm2

Follow-Up Questions

Answer the following questions on loose leafand hand them in to your teacher.

Follow-Up Questions

17 m

23 m

1) Find the perimeter of each figure.

a)

b)

8 in

c)

5 cm

12 cm

13 cm

d) 9 ft

15 ft

6 ft4 ft 4 ft

Follow-Up Questions

14 m

14 m

2) Find the area of each figure.

a)

b)11 in

c)

18 cm

12 cm15 cm

d) 9 ft

15 ft

6 ft4 ft 4 ft