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 R\(_{1}\) and R\(_{2}\) that enclose no common region then

ar (region R) = ar(region R\(_{1}\)) + ar(region R\(_{2}\)).

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






9th Grade Math

From Area of a Closed Figure to HOME PAGE


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.



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.



Share this page: What’s this?

Recent Articles

  1. Fraction as a Part of Collection | Pictures of Fraction | Fractional

    Feb 24, 24 04:33 PM

    Pictures of Fraction
    How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

    Read More

  2. Fraction of a Whole Numbers | Fractional Number |Examples with Picture

    Feb 24, 24 04:11 PM

    A Collection of Apples
    Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

    Read More

  3. Identification of the Parts of a Fraction | Fractional Numbers | Parts

    Feb 24, 24 04:10 PM

    Fractional Parts
    We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

    Read More

  4. Numerator and Denominator of a Fraction | Numerator of the Fraction

    Feb 24, 24 04:09 PM

    What are the numerator and denominator of a fraction? We have already learnt that a fraction is written with two numbers arranged one over the other and separated by a line.

    Read More

  5. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 24, 24 10:59 AM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More