Area

The amount of surface that a plane figure covers is called its area. It’s unit is square centimeters or square meters etc.

We can find the area of the surface enclosed, by finding the number of complete unit squares inside the figure drawn on a square sheet. The unit of area is square centimeter. 

A rectangle, a square, a triangle and a circle are all examples of closed plane figures.

In the following figures, the shaded region of each of the object is the surface occupied by it. We call it area.

Interior and Exterior of a Region

The part of the plane enclosed by a closed figure is called the interior region and the part of the plane outside the enclosed figure is called the exterior region.

Interior and Exterior of a Region

In the adjacent figure a rectangle ABCD is shown. It’s interior and exterior regions are also shown here.


Area is always measured in squares and the unit of area square units (sq. cm., sq. m. or cm2, m2).

Let us draw some plane shape on a square sheet as shown below.

Area of Plane Shapes

Here, we can see that the shape at figure (i) is the smallest in size or we can say that it encloses least space or surface than figure (ii) and figure (iii). Let us compare the surface of paper enclosed by each shapes. The shape at figure (i) encloses only one unit square on the graph sheet. The shape at figure (ii) encloses 4 unit squares and the shape at figure (iii) encloses 9 unit squares on the graph sheet. We observe that larger shapes encloses more surface than the smallest shapes. The surface enclosed by a plane shape is called its area.


Measuring Regions:

We know that a flat surface is called a plane. A square, a triangle and a circle are some examples of plane shapes. The amount of surface enclosed is called its area. We can calculate the area of a plane shape drawn on a square sheet by counting the unit squares enclosed by it.

For irregular shapes, we count 2 half squares as one and ignore those squares whose less than half part is enclosed by the figure.


Unit of Area:

The area is measured in square units. A square of side 1 cm or 1 m is used as standard units. Smaller unit of area is square cm or sq. cm. Bigger areas are measured in meters and kilometers.

We measure a given region by a unit region and find how many such unit regions are contained in the given region.

Unit Region

The measure of a region is called its area.

The area is always expressed in square units. The standard units that are generally used for measuring area are square centimeter and square meter.

The area of a square with side 1 cm each is 1 cm × 1 cm = 1 square centimeter. In short, it is expressed as cm2 or sq. cm.

The area of a square with side 1 m each is 1 m × 1 m = 1 square meter. In short, it is expressed as m2 or sq. m.

10 Square Unit
5 Square Unit

Area is a measure of any area surface, e.g., the surface of a table, the surface of your pencil box etc.


Area is two dimensional.

It means, to find the area of any surface we need to know two sides.

Note: Here we’ll discuss only areas of square and rectangles. Given below is a table of units of sides and corresponding units for areas.

Units to Find Area

Conversion Table:

1 m. = 100 cm.

1 sq. m. = 10000 sq. cm.

1 cm. = 10 mm.

1 sq. cm. = 100 sq. mm.

1 km = 1000 m

For finding the area of a given figure, make sure that the sides (length or breadth) are in the same unit of length. If they are given in different units, change them to the same unit.


Solved Examples on Measuring Regions:

1. Find the area of the figures given on a graph sheet of 1 cm × 1 cm squares.

Solution:

Figure (i):

                 \(\frac{1}{2}\)  squares = 6; Full Squares = 6

                 Area = \(\frac{1}{2}\) × 6 + 6 = 9 sq. cm.


Figure (ii):

                 Number of Squares = 12

                 Area = 12 sq. cm.


2. Find the area of following figures on the graph sheet of 1 cm square.

Area of Figures

There are 4 squares in figure (i).

So, the area of figure (i) is 4 sq. cm

There are 8 squares in figure (ii).

So, the area of figure (ii) is 8 sq. cm


Now, answer the following questions to have a quick review of what we have learnt so far.

1. For the given figures find the area of each figure if each side of a square is 1 unit.

Find the Area of each Figure

Answer:

(i) 32 sq. units

(ii) 26 sq. units


2. If area of each square is 1 square cm find the area of the given figures.

(i) Area =

Area of Each Square

(ii) Area =

Area of the Given Figure


(iii) Area =

Find the Area of the Given Figure

(iv) Area =

Area of the Given Figures

Answer:

(i) 40 sq. cm

(ii) 36 sq. cm

(iii) 22 sq. cm

(iv) 20 sq. cm


3. Draw any three polygons of the largest possible size in the given grids and calculate their area if each side of a square is 1 cm.

Grids and Area

4. Draw any shapes in the grids with the following area if each side of a square is 1 unit.

(i) Area = 9 square units

Area = 9 Square Units

(ii) Area = 20 square units

Area = 20 Square Units

(iii) Area = 15 square units

Area = 15 Square Units


5. Fill in the blanks:

(i) …………………….. measures the surface covered by a 2D shape.

(ii) The area of a rectangle with length 5 m and breadth 10 m will be ……………………..


Answer:

(i) Area

(ii) 50 sq. units

You might like these

Area.

Area of a Rectangle.

Area of a Square.

To find Area of a Rectangle when Length and Breadth are of Different Units.

To find Length or Breadth when Area of a Rectangle is given.

Areas of Irregular Figures.

To find Cost of Painting or Tilling when Area and Cost per Unit is given.

To find the Number of Bricks or Tiles when Area of Path and Brick is given.

Worksheet on Area.

Worksheet on Area of a Square and Rectangle

Practice Test on Area.








5th Grade Geometry

5th Grade Math Problems

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