Loading [MathJax]/jax/output/HTML-CSS/jax.js

Area of a Closed Figure

We will discuss here about the area of a closed figure, measurement of area, area axiom for rectangle, area axiom for congruent figures and addition axiom for area.


Area of a closed figure

The measure of the reason bounded by a closed figure in a plane is called its area. In the following the areas of the figures are shaded.


Measurement of area

The area of a square of sides of length 1 unit is called an area of 1 unit2. The area of a closed figure is measured by the number of unit squares contained in the region.

Area axiom for rectangle

The area of a rectangle is the product of its length and breadth. PQRS is a rectangle region. Its area = PQ × QR.


Area axiom for congruent figures

Any two congruent figures have equal area.

Let ∆PQR ∆XYZ. Then the area of the ∆PQR is equal to the area of the ∆XYZ.

We write ar(∆PQR) for the area of the ∆PQR.

Therefore, ∆PQR ∆XYZ     ⟹ ar(∆PQR) = ar (∆XYZ).

In the same way, if two polygons are congruent then their areas will be equal.

Note: Two triangles (or closed figures) may have equal areas but they may not be congruent.


Addition axiom for area

If a closed reason R is divided into two regions R1 and R2 that enclose no common region then

ar (region R) = ar(region R1) + ar(region R2).

Here, ar(quadrilateral PQRS) = ar(∆PQS) + ar(∆QRS).






9th Grade Math

From Area of a Closed Figure to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Counting Numbers from 1 to 50 | Match the Number | Missing Numbers

    Apr 04, 25 03:46 PM

    Math Coloring Pages on Counting Number Oredr
    In counting numbers from 1 to 50, recognize the numbers, count and then join the numbers in the correct number order. Here we mainly need eye-hand coordination to draw the picture and maintain the num

    Read More

  2. Counting Eleven to Twenty with Numbers and Words |Numbers from 11 - 20

    Apr 04, 25 03:21 PM

    Counting eleven to twenty with numbers and words are explained below. One ten and one more is eleven. Eleven comes after ten. One ten and two more is twelve. Twelve comes after eleven.

    Read More

  3. 5th Grade BODMAS Rule Worksheet | PEMDAS | Order of operations|Answers

    Apr 03, 25 03:11 PM

    5th Grade BODMAS Rule Worksheet
    In 5th Grade BODMAS Rule Worksheet you will get different types of problems on mathematical expressions involving different operations, mathematical expression with 'brackets' and 'of' and simplifying…

    Read More

  4. Worksheet on Simplification | Simplify Expressions | BODMAS Questions

    Apr 03, 25 02:58 PM

    Worksheet on Simplification
    In worksheet on simplification, the questions are based in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. This exercise sheet

    Read More

  5. Divisible by 2 Video |Test of Divisibility by 2 Trick| Rules| Examples

    Apr 03, 25 10:25 AM

    Divisible by 2
    A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.

    Read More