What is Area in Math? Definition, Formulas, Shapes, Examples (2023)

Definition

Definition

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area.

Now, imagine your square is made up of smaller unit squares. The area of a figure is counted as the number of unit squares required to cover the overall surface area of that particular 2-D shape. Square cms, square feet, square inches, square meters, etc., are some of the common units of area measurement.To find out the area of the square figures drawn below, draw unit squares of 1-centimeter sides. Thus, the shape will be measured in cm², also known as square centimeters.

Here, the area of the shapes below will be measured in square meters (m²) and square inches (in²).

How to calculate the area if there are also half unit squares in the grid?

To understand that, let us take one more example:

Step 1: Count the full squares.

There are 18 full squares.

Step 2: Count the half squares.

On counting, we see that there are 6 half squares.

Step 3: 1 full square $= 1$ square unit

So, 18 full square $= 18$ square units

1 half square $= \frac{1}{2}$ square unit

6 half squares $= 3$ square units

Total area $= 18 + 3 = 21$ square units.

Origin of the Term: Area

The term ‘area’ originated from Latin, meaning ‘a plain piece of empty land’. It also means ‘a particular amount of space contained within a set of boundaries’.

Look at the carpet in your home. To buy a carpet that fits the floor, we need to know its area. Or the carpet will be bigger or smaller than the space! Some other instances when we need to know the area are while fitting tiles on the floor, painting the wall or sticking wallpaper to it, or finding out the total number of tiles needed to build a swimming pool.

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Formulas for Calculating Area

We are surrounded by so many 2-D shapes: circle, triangle, square, rectangle, parallelogram, and trapezium. You can draw all of these shapes on your paper. Every shape is different and unique, so its area is also calculated differently. To find the area, first, identify the shape. Then, use the appropriate formula from the list given below to find its area.

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Areas of Composite Figures

Every plane figure cannot be classified as a simple rectangle, square, triangle, or typical shape in real life. Some figures are made up of more than one simple 2-D shape. Let us join a rectangle and a semicircle.

These shapes formed by the combination of two or more simple shapes are called “composite figures” or “composite shapes”.

For finding the area of a composite figure, we must find the sum of the area of all the shapes in it. So, the area of the shape we just drew will be the area of the rectangle, l$\times$ b plus half the area of the circle, ½ x πr², where l and b are length and breadth of the rectangle and r is the radius of the semicircle.

If we draw a semi – circle below a triangle, we get the composite shape:

The area of such a composite figure will be calculated by adding the area of the triangle and the area of the semicircle.

Area of the a composite figure =($\frac{1}{2}\times b\times h) (\frac{1}{2}+𝜋r^2$)

where r is the radius of the semicircle and b and h are the base and height of the triangle respectively.

Real-life Applications

Here are a few ways in which you can apply the knowledge of the area of figures in your daily life.

• We can find the area of a gifting paper to check whether it will be able to cover a box or not.
• We can find the area of a square or circle to find the area of the signal board.

Solved Examples

1. A circle has a diameter of 20 cm. Find out the area of this circle.

Ans: For the circle, d = 20 cm.

Radius, r = $\frac{d}{2}$ = 10 cm

Therefore, A = πr²

= 3.14$\times 10\times 10$ = 314 cm$^{2}$

Area of the given circle is 314 $cm^{2}$.

1. The height of a triangle is 10 cm and the base is 20 cm. What is the area of this triangle?

Ans: Area of the triangle = $\frac{1}{2}\times b\times h$

= $\frac{1}{2}\times 20\times 10 = 100 cm^{2}$

Therefore, the area of the given triangle is 100 $cm^{2}$.

1. The width of a rectangle is half of its length. The width is measured to be 10 cm. What is the area of the rectangle?

Ans: For the rectangle, w = 10 cm and l = (10 $\times$ 2) = 20 cm.

(Video) 3. AREA of all SHAPES Mathematics Formula

Area of the rectangle, i.e., A = l $\times$ w

A = 20 $\times$ 10 = 200 cm$^{2}$

Therefore, the area of the given rectangle is 200 cm$^{2}$.

Example 4: What is the area of the following figure?

Solution: Full square $= 1$ square unit

So, 14 full square $= 14$ square units

1 half square $= \frac{1}{2}$ square units

5 half squares $= 2.5$ square units

Total area $= 14 + 2.5 = 16.5$ square units.

Practice Problems

1

The side of a square is 7 cm. What is the area of this square?

20 cm$^{2}$

30 cm$^{2}$

40 cm$^{2}$

49 cm$^{2}$

CorrectIncorrect

Correct answer is: 49 cm$^{2}$
Area of the square = side $\times$ side A = 7 $\times$ 7 = 49 cm$^{2}$

2

The height of a triangle is 25 cm and the base is 50 cm. What is the area of the triangle?

600 cm$^{2}$

(Video) Introduction to Area and Area Formulas

625 cm$^{2}$

650 cm$^{2}$

700 cm$^{2}$

CorrectIncorrect

Correct answer is: 625 cm$^{2}$
Area of the triangle = $\frac{1}{2}\times b\times h = \frac{1}{2}\times 50\times 25$ = 625 cm$^{2}$

3

What is the area of a circle that has a radius of 4 cm?

40 cm2

16 cm$^{2}$

60.27 cm$^{2}$

50.27 cm$^{2}$

CorrectIncorrect

Correct answer is: 50.27 cm$^{2}$
Area of the circle = 𝜋r$^{2}$ = 3.14$\times 4\times 4$ = 50.27 cm$^{2}$

4

The base of a parallelogram is 50 cm and the perpendicular height is 20 cm. What is the area of this parallelogram?

400 cm$^{2}$

500 cm$^{2}$

750 cm$^{2}$

1000 cm$^{2}$

CorrectIncorrect

Correct answer is: 1000 cm$^{2}$
Area of the parallelogram = b$\times$ h = 50$\times$ 20 = 1000 cm$^{2}$

(Video) Calculating the Area of Shapes

Conclusion

Through SplashLearn, learning becomes a part of children’s lives, and they get encouraged to study every day. The platform does this through interactive games and fun worksheets. For more information about exciting math-based games, log on to www.splashlearn.com.

Related math vocabularyLearn more about concepts like Perimeter, Polygon, Square Unit, Unit Square and more such exciting mathematical topics at www.SplashLearn.com.

Perimeter and area are related to the 2-D geometry of shapes. Perimeter is the total length of the outline around the shape, while area is the total space inside the shape.

Area is a measure of the number of unit squares that fit in a 2-D shape, so it is expressed in square units. Perimeter is the measure of the length of the outline of the shape and is expressed in linear units.

The knowledge of the area of a shape gives students a clear understanding of the total space covered within the boundary of that shape. This concept has many real-life applications, like finding the carpet area of a room, finding the total size of the wall that needs to be painted, etc.

Divide the irregular shape into unit squares and calculate the total number of unit squares. If a few unit squares are not occupied entirely, approximate to 0 or 1 for each.

(Video) Formulas of all Shapes | Area formulas | Easy maths | True Academy

FAQs

What is area in math and example? ›

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares.

What is area definition and formula? ›

Area = length x breadthArea = l × b. Area = π × radius × radiusArea = π × r2(π = 3.14) Using these formulas, area for different quadrilaterals (a special case of polygons with four sides and angles ≠ 90o) is also calculated. Application. The concept of area is the foundation of geometry since the early days.

What is the area of a shape example? ›

Area is calculated by multiplying the length of a shape by its width. In this case, we could work out the area of this rectangle even if it wasn't on squared paper, just by working out 5cm x 5cm = 25cm² (the shape is not drawn to scale).

What is definition of area in math? ›

What is Area? The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

What are the 2 formulas for area? ›

Area Formulas
FiguresFormulaVariables
RectangleArea = l × wl = length w = width
SquareArea = a 2a = sides of square
TriangleArea = 1 2 bhb = base h = height
CircleArea = π r 2r = radius of circle
2 more rows

What is the formula for area answer? ›

The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.

What is the formula of area formula? ›

Area formula for few shapes is given as, Area of square = (side) Area of rectangle = length × breadth. Area of triangle = (1/2) × base × height.

How do you find the area of all shapes? ›

How to calculate area?
1. Square area formula: A = a²
2. Rectangle area formula: A = a × b.
3. Triangle area formulas: A = b × h / 2 or. ...
4. Circle area formula: A = πr²
5. Circle sector area formula: A = r² × angle / 2.
6. Ellipse area formula: A = a × b × π
7. Trapezoid area formula: A = (a + b) × h / 2.
8. Parallelogram area formulas:
Nov 2, 2022

What is an example of an area of a rectangle? ›

The formula for finding the area of a rectangle

For example, if the length of a rectangle is 35 m and width is 25 m, then the area is 35 × 25 = 875 square meters.

What shapes use the area formula? ›

Perimeter, Area, and Volume
Table 2. Area Formulas
ShapeFormulaVariables
SquareA=s2s is the length of the side of the square.
RectangleA=LWL and W are the lengths of the rectangle's sides (length and width).
TriangleA=12bhb and h are the base and height
4 more rows

What does area mean in math 7th grade? ›

The area in maths is the amount of space taken up by a 2D shape.

What is area in math 3rd grade? ›

Area refers to the amount of space a two-dimensional figure takes up. One-dimensional figures have no volume. One can find the area of a rectangle by counting individual square units or by multiplying the length and width of the figure.

How do you find area 5th grade? ›

Use the formula Area = (Length) x (Width). Since the classroom is 20 feet long and ten feet wide, multiply 20 feet by ten feet to get the area of 200 square feet (20 x 10 = 200).

What is the example of area of square? ›

The area of a square is equal to (side) × (side) square units. The area of a square when the diagonal, d, is given is d2÷2 square units. For example, The area of a square with each side 8 feet long is 8 × 8 or 64 square feet (ft2).

How do you find the area of a circle? ›

The area of a circle is pi times the radius squared (A = π r²).

What was the area of a triangle? ›

Thus, the area of a triangle is half the product of its base and height. Area of a triangle = ½ × base × height.

What are the basic area formulas? ›

Basic Geometry - Area Formulas
• Area of a Rectangle = Base × Height.
• Area of a Square = Base × Height.
• Area of a Square = s2
• Area of Triangle = ½(Base × Height)
• Area of Parallelogram = Base × Height.
• Area of Trapezoid = ½(Base1 + Base2) × Height.
• Area of Circle = π(radius)2 = πr2

Does area mean divide or multiply? ›

And, more generally, the area of any rectangle can be found by multiplying length times width. A rectangle has a length of 8 centimeters and a width of 3 centimeters. Find the area. Start with the formula for the area of a rectangle, which multiplies the length times the width.

What is the symbol for area? ›

Area
Common symbolsA
SI unitSquare metre [m2]
In SI base units1 m2
Dimension
1 more row

Is area adding or multiplying? ›

The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.

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