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

    Apr 03, 25 02:56 AM

    5th grade bodmas rule worksheet

    Read More

  2. Before and After Video | Math Worksheets on Number | Before and After

    Apr 03, 25 12:44 AM

    before and after number worksheet
    Free math worksheets on numbers before and after help the kids to check how much they are good at numbers. The purpose of this math activity is to help your child to say a number in order and also hel

    Read More

  3. Order of Numbers Video | Before and After Numbers up to 10 | Counting

    Apr 03, 25 12:39 AM

    We will learn the order of numbers in a number line. In numbers and counting up to 10 we will learn to find the before and after numbers up to 10.

    Read More

  4. Counting Before, After and Between Numbers up to 10 Video | Counting

    Apr 03, 25 12:36 AM

    Before After Between
    Counting before, after and between numbers up to 10 improves the child’s counting skills.

    Read More

  5. Numbers and Counting up to 10 | Why do we Need to Learn Numbers?|Video

    Apr 03, 25 12:33 AM

    Learning Numbers
    We will learn numbers and counting up to 10 to recognize the numerals 1 through 10. Counting numbers are very important to know so that we can understand that numbers have an order and also be able to

    Read More