Copyright

Comparing Measurement of Shapes

Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education

There are a wide variety of geometric shapes. There are equations to determine their perimeters and areas. In this lesson, we will explore different shapes and compare their perimeters and areas.

Measurements

When you go to the doctor, it is common for them to measure your height and weight. Let's pretend you are 5 feet tall and weigh 95 pounds. Your friend is 4 feet 6 inches tall and when he gets on the scale you see he weighs the same amount! People come in all shapes and sizes, and so do geometric shapes. Let's look at a few geometric shapes and show that they can be different shapes, but with the same areas or perimeters.

Rectangles and Triangles

A rectangle is a four-sided shape with all of the angles equaling 90°. Their adjacent sides are not equal in length.


A rectangle
rectangle


Let's compare a rectangle to a right triangle. A right triangle is a three-sided shape with one 90° angle. If you add all of the angle values you will get 180°.


A right triangle
rt


The perimeter of a shape is the distance around the outside of the shape. The perimeter of a rectangle is the sum of the length of the four sides. The perimeter of a right triangle is the sum of the length of the three sides. Let's look at Diagram 1, which shows the lengths of each side of a rectangle and triangle.


Diagram 1
compare1


Let's determine both of their perimeters by adding all of the lengths of their sides. We will use the metric unit centimeters to represent length. (The diameter of a penny is roughly a centimeter.)

Perimeter of Rectangle:

7 cm + 5 cm + 7 cm + 5 cm = 24 cm

Perimeter of Right Triangle:

12.2 cm + 10 cm + 7 cm = 29.2 cm

We can see the perimeters are not equal. Now let's determine their areas. Area is the amount of two-dimensional space a shape occupies. The area of a rectangle is length multiplied by width. The area of a triangle is one-half of the base multiplied by the height. Both areas will be in the metric unit square centimeters (cm2).

Area of Rectangle:

7 cm × 5 cm = 35 cm2

Area of Right Triangle:

(1/2) × (10 cm) × (7 cm) = 35 cm2

The area of both of these shapes is the same! This proves that different shapes with different perimeters can have the same area. Let's do another example.

Circle and Sphere

A circle is a two-dimensional shape with no sides, and a continuous curve with one radius all the way around the circle such as a Frisbee.


Circle
circle


A sphere is a three-dimensional shape with no sides, and a continuous curve with one radius all the way around the sphere (like a basketball).


Sphere
sphere


The perimeter around either a circle and a sphere is called the circumference (C) and they both have the same equation! C = 2 × π × r. We will estimate π to be 3.14. Let's compare a circle and a sphere. They both have a 2 cm radius. Diagram 2 shows these shapes.


Diagram 2
circle_sphere


If their radii are the same, and the equations for their circumferences are the same, their circumferences are the same. This means if a bug were to walk around the edge of a circle and around the outside of a sphere, they would walk the same distance. Let's prove it.

Circumference of Circle:

2 × 3.14 × 2 cm = 12.56 cm

Circumference of Sphere:

2 × 3.14 × 2 cm = 12.56 cm

We were correct with our prediction! Both circumferences are the same.

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account
Support