Skip to content

Online Math Center

Home The Basic Geometrical Shapes in Math

The Basic Geometrical Shapes in Math

The Basic Geometrical Shapes in Math

Geometry can be considered the fun part of mathematics due to the drawings we have to make based on calculus. It’s quite fascinating to see how a certain number indicates an angle or where multiple lines meet and become a shape. 

The basic shapes in mathematics are taught in middle school even though students should be able to recognize them already from games that enhance visual memory. 

Let’s make sure you memorize the fundamental geometrical shapes so you can, later on, solve complex geometry problems.  


The 5 most common geometric shapes

These shapes have built up the world. You can see them on the street, in the architecture of buildings, in the structure of your furniture or your jewelry. The world has been built on: circles, squares, rectangles, and triangles. 


The Circle

geometrical shapes in math

A circle is a geometrical shape that we can create by drawing a curved line from one end to another, respecting the same distance around a specific point (center of the circle).

 

When we calculate the dimensions of a circle, we refer to its: circumference, center, radius, chord, and diameter.

 

Circumference: The circumference of a circle refers to the numerical value of the outer line of the circle.

 

How do we calculate the circumference? 

In order to determine the circumference of a circle, we need to know its diameter or radius. Thus, we have the following formulas:

 

C = 𝝿 d, where C is the circumference,  𝝿 is 3.14159 and d is the diameter.

 

Or,

 

C = 2𝝿 r, where C is the circumference,  𝝿 is 3.14159 and r is the radius. 

 

Chord: The chord of a circle refers to any segment or line drawn from one point of the circle to another point of the circle. The diameter of the circle would be the longest chord. 

 

The length of the chord is calculated with this formula: 2 x (r2– d2)

geometrical shapes in math

Center

 

The center of a circle is the point from which all the points on the circle are at the same distance. 

 

How can we find the center of a circle? 

 

In order to find the center of a circle, we need to draw a chord. Name the first chord AB for keeping track easily. Draw a second chord, parallel and of the same length as AB, and name it CD. Unite the points in a cross: A to D, and B to C.

 

The intersection point should be the center of the circle. 

geometrical shapes in math

Diameter: is the chord that passes through the center of the circle, thus making it the longest chord.

The diameter of a circle is 2 x the radius of a circle. 

Diameter’s formula: D = 2r. 

        D = C𝝿, where C is the circumference of the circle and 𝝿 (pi) is 3.14159. 

Or, in case we know the area of a circle, we use the formula: 

        D = 2A𝝿  , where A is the area divided by 𝝿 (pi) = 3.14159

The radius is a segment or a line drawn from the center of a circle to any point on the circle. 

When we know the circumference of the circle, we can calculate the radius with the next formula: r = C2𝝿 

If we know the area of the circle, we use the following formula: r = A𝝿

Or, if we know the diameter, we simply divide the diameter by 2. 

 

The Square

A square is a geometrical shape formed of 4 parallel and equal lines. The 4 lines form 4 equal right angles of 90° each.

   

The square has three elements: area, diagonal, and perimeter.

geometrical shapes in math

The Area is the total of the side lengths of a square. 

We can determine the area of a square, by using this simple formula:  Area (A) = a2 = a × a

 

The perimeter of a square is the outer length around the square, just like the circumference of a circle. 

We can calculate the perimeter of a square by this formula: P = 4a, a being the sideline of the square. 

 

The diagonal of a square is the line that cuts the square into two equal triangles from one corner to another. A square has two equal diagonals, which intersect in the middle. 

The formula for the diagonal is d = a × 2 , where a is the sideline of a square. 

 

The Rectangle

A geometrical shape with 4 lines of 2 different and equal dimensions. The opposite sides are parallel and of equal length.

 

Similar to the square, we can calculate the area, perimeter and diagonals of a rectangle. 

 

The formula of the area of a rectangle is: a x b, where a is one of the longest side lines and b is one of the shortest side lines. 

geometrical shapes in math

Formula for a rectangle’s perimeter: 2 (a+b).

Formula for a rectangle’s diagonal: (a2+ b2), a rectangle has two diagonals of identical lengths which intersect in the middle. 

 

The Triangle

A triangle is a geometric figure composed of three side lines and three angles. 

There are 3 types of triangles: equilateral, isosceles and scalene. Each of these types comes with some particularities. We can also differentiate triangles according to their specific angles, there are: 

 

  1. Acute triangles with ALL angles < 90°.
  2. Right triangles with ONE right angle = 90°.
  3. Obtuse triangle with ONE angle > 90°.
 

Measuring triangles and calculating laterals and angles of triangles has been a great part of geometry.

Pythagora even came up with a special theorem about triangles, therefore, the OMC math tutors will dedicate a whole article to triangles for math-lovers, so stay close to us.

 

Follow our blog for more useful and fun information on mathematics. 

 

Ready to learn more math? Our OMC math tutors offer individual and group math lessons to middle school students.

 

Contact us for a tailored math tutoring plan, anytime! 

Step Two

Let us know how to contact you. One of our representatives will get back to you shortly.

    By clicking the «Try it» button, you agree to our Terms of Use and Privacy Policy*

    Step Two

    Awesome! We need to get in touch with your parent or guardian for further discussion. Please check in with them before filling out the form below with their information.

      By clicking the «Try it» button, you agree to our Terms of Use and Privacy Policy*

      Step One

      It only takes two steps to schedule an appointment with an OMC representative.

       

      To get started, please tell us who you are:

      Thank you!

      Please check your inbox for more information about your lesson.

       

      If you did not receive a message from us, please check your email’s “Spam” folder.

      Dear Parent!

      Thank you for placing your trust in us to educate your child!
      Please check your inbox for more information about your child’s program and schedule.

      Congratulations on joining the Online Math Center!
      See you in class.

      Step One

      It only takes two steps to schedule a free lesson with an OMC representative.


      To get started, please tell us who you are:

      Payment

      0%
      0%

      Error: Contact form not found.

      By clicking the «PAY» button, you agree to our Terms of Use and Privacy Policy*

      Payment amount: $323.00

      Secure payments by Stripe.

      We do not collect your credit card on our servers.

      Thank you!

      Our manager will be in contact with you shortly.

       

      Please check your inbox for more information. If there is no message from us, please check your email’s “Spam” folder.