Area of Geometric shapes

Area of Shapes

The area of shapes is the space surrounded or enclosed with the boundary of perimeter of the given geometric shapes. It is a measurement that determines the magnitude of two-dimensional shape or planar lamina in the plane. The shape of the lamina includes two-dimensional figures that can be easily drawn on the plane such as square, rectangle, triangle, parallelogram, trapezium etc. Areas of shapes such as square, rectangle, triangle, parallelogram, trapezium, circle are the range covered by them in space. In this article you will study areas of geometric shapes, area formulas for different shapes, area of 2d shapes, area of 3d shapes etc.

Polygon Shapes 

A polygon is a two-dimensional shape that is made up of straight lines. Some examples of polygon shapes are triangle, pentagon, hexagon, square, rectangle, etc. The name of these shapes itself determines the total number of sides included in the shape. For example- a triangle has 3 sides and a rectangle has 4 sides. Therefore, any shape that is made up of joining three lines is known as a triangle whereas the shapes that are made up of joining four lines are known as quadrilaterals. The area is the range inside the boundary/perimeter which is to be examined.

Area of 2d Shapes

In geometry, two-dimensional shapes are defined as the flat plane figure or shape that includes two measures such as length and breadth. There is no thickness in 2-d shapes. Area and perimeter are two different measures used for measuring flat shapes. The two-dimensional can be easily drawn on a plain paper. Some of the examples of 2-d shapes are rectangle, triangle, square, trapezoid etc.

Area of 2d Shapes Formula-

Generally, the area of shapes is defined as the quantity of paint color required to cover any of the surface with a single coat. Here are the methods to calculate area on the basis of sides included in the shape as described below:

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Here, you can see the Area Formulas for Different Shapes in Tabular Format.

Shapes

Area

Terms

Circle

π × r²

R indicates the radius of a circle

Triangle

½ × b × h

B indicates breadth whereas h indicates height

Rectangle

L  × w 

L indicates length whereas w indicated width

Parallelogram 

b  × h

B indicates breadth wheeras h the indicates height 

Trapezium 

½ (a+b)  × h

(a+b) are the length of the parallel sides whereas h is the height of the trapezium

Ellipse

Π ab

Here,

A = ½ minor axis

b= 1/2 minor axis


Area of 3d Shapes

Three-dimensional shapes are the solid shapes that retain three-dimensions such as length, width and height.The two different measures used to determine three-dimensional   shapes are volume and surface area. Generally, we get the three-dimensional  shapes from the rotation of the two-dimensions shapes. The major difference between 2-d and 3-d shapes is that the 3-shapes have thickness whereas 2-d shapes do not have thickness. If you want to determine the surface area of any solid shapes, then it can be easily determined from the area of 2 d shapes.

Area of 3D Shapes Formula-

According to the international system of units (SI), the standard unit of area is meter square(m²). For example- a certain shape with an area of 4 square meters will have the similar areas as four such squares. The surface area of solid shapes is determined as a measure of a total area that the surface of the object covers.

Here, you can see the Area Formulas for all Shapes in Tabular Format.

Shapes

Formula

Terms

Cube

6a²

‘a’ = length of the edge

Rectangular prism 

2(wl +hl + hw)

1= length, w= width, h=height 

Cylinder

2Π r (h + r)

r = radius if the circular base

h= height of the cylinder

Cone

Πr ( r + l)

r = radius if the circular base

L = slant height

Sphere

4Πr²

r = radius of spheres

Hemisphere

3Πr²

r= radius of the hemisphere


Including the area of the planar shapes, an extra variable i.e the height of the variable is taken into consideration for calculating the surface area of shapes.

Examine a circle of radius r and draw boundless concentric circles.Now, from the center of a circle to its boundary , draw a line segment equivalent to the radius of a circle along with that segment. A triangle will be formed with a  base equivalent to the circumference of a circle  and height equivalent to the radius of the outer circle i.e. r. Thus the area can be calculated as ½ × base × height  ie. ½ * 2πr².

Solved Examples-

1. Calculate the Area of the Circular Path whose Radius is 7cm.

Solution: 

Radius of circular path = 7 cm (given)

As we know, the area of a circle is πr²

Accordingly,

 Area = π × r × r

Area = 22/7 × 7 × 7

Area = 154 square metre

2. What will be the Breadth of a Rectangle, if its Area is 72cm and Length is 8 cm.

Solution:

As we now,

Area of a rectangle =  length × breadth

Given that , area= 72cm and length = 8 cm

Let the breadth of a rectangle be a

As we now,

Area of a rectangle =  length × breadth

Accordingly,

A =  l × b

72 = 8 × a

72= 8a

a = 72/9

a= 8 cm

Hence, the breadth of a rectangle 8 cm.

3. Calculate the Area of a Cone whose Radius is 4cm and Height s 3cm’

Solution:

Radius of a cone = 4cm and height of a cone= 3 cm ( Gven)

As we now, the area of the cone is πr(r + l)

Slant height= l \[\sqrt{4²+3²}\] =   \[\sqrt{25}\] = 5cm

Area of a cone = πr(r + l)

A = 22/7 × 4 (4 + 5)

A = 22/7 × 4(9)

A= 22/7 × 36

A = 113.14 cm²

Quiz Time

1. Two Equivalent Parallelograms have their Corresponding Sides in the Ratio of  1 : k.what will be the Ratio of their Areas.

  1. 1:3²

  2. 1:4²

  3. 1:k²

  4. 1:2k²

2. How will the Surface Area of a Sphere Change, if the Diameter of the Spheres is Doubled?

  1. It will increase two times

  2. It will increase three times

  3. It will increase four times

  4. It will increase eight times

3. What will be the Area of a Rectangle whose Altitude is Equal to 2\[\sqrt{3}\]cm

  1. \[\sqrt{3}\]cm²

  2.  2\[\sqrt{3}\]cm²

  3. 3\[\sqrt{3}\]cm

  4. 4\[\sqrt{3}\]cm²

FAQ (Frequently Asked Questions)

1. Why do we Learn the Perimeter and Area Formulas for all Shapes?

As we know, that area is basically the space covered by the geometric shapes and the perimeter is the distance around the shapes. If you want to paint your house, you should know the area of the house to calculate the quantity of paint required and the cost of  the paint.


For instance, to fence your garden, you should know the length of the sides or perimeter of the garden to calculate the material required for fencing. The garden is square in shape with each in cm and premiere would be 4a cm. The area is the space included in the shape or given figure. It is calculated in square units. Suppose you want to fix tiles in your home, you should know the area of the floor to know the no. of tiles required to cover the whole floor.