Area	Surface Area
Area of a plane object is the number of unit squares that can be accommodated within it.	Total area of the faces of a 3 – dimensional object.
Plane figures represent the area. Like circles, rectangles and triangles.	Solid figures represent the surface area. Like prisms, pyramids and cones.
Formula of area for the rectangle is – length multiplied by width.	Formula to calculate the surface area for a cuboid is = 2lw + 2lh + 2hw.
Area is the measurement of the size of a 2-D figure	Surface area is the measurement of the size of a 3-D figure.
It expresses the size measurement of a surface.	It expresses the measurement of the exposed surface of a solid object.
When it comes to the area, all we have to do is concentrate on one area.	In the surface area, we have to work out on the area of all the faces

Let’s clarify the difference between area and surface area with a focus on their examples:

Example of Area

Area refers to the measurement of a flat, two-dimensional surface. It quantifies the extent of a surface within its boundaries. This concept is used for shapes and figures that lie on a plane.

Example: Area of a Rectangle

Imagine a simple rectangular garden with the following dimensions:

• Length: 10 meters
• Width: 6 meters

To find the area of this rectangle: Area= Length× Width

Area = 10 meters × 6 meters

= 60 square meters

This calculation tells us the total space available within the rectangle, which is 60 square meters.

Example of Surface Area

Surface Area refers to the total area of the outer surface of a three-dimensional object. It encompasses all the faces of the object. This measurement is important for objects that have depth or height in addition to length and width.

Example: Surface Area of a Rectangular Prism (Cuboid)

Consider a rectangular prism (cuboid) with dimensions:

• Length: 10 meters
• Width: 6 meters
• Height: 4 meters

To calculate the surface area of this cuboid, you need to find the area of all six faces:

Top and Bottom Faces: Both are rectangles with dimensions 10 meters by 6 meters.

Area of Top and Bottom Faces = 2×(10 meters×6 meters)

= 2×60 square meters

= 120 square meters

Front and Back Faces: Both are rectangles with dimensions 10 meters by 4 meters.

Area of Front and Back Faces = 2×(10 meters×4 meters)

= 2×40 square meters

= 80 square meters

Left and Right Faces: Both are rectangles with dimensions 6 meters by 4 meters.

Area of Left and Right Faces = 2×(6 meters×4 meters)

= 2×24 square meters

= 48 square meters

Add all these areas together to get the total surface area:

Surface Area = 120 square meters + 80 square meters + 48 square meters

= 248 square meters

Key Differences Between Area and Surface Area

Dimensionality

• Area: Measures space in two dimensions (e.g., length and width). It applies to flat shapes.
• Surface Area: Measures space in three dimensions (e.g., length, width, and height). It applies to objects with depth.

Application

• Area: Used for determining the size of flat surfaces, like the area of a garden or a painting.
• Surface Area: Used for determining the total area that covers a three-dimensional object, like the amount of paint needed for a box or the wrapping paper for a gift.

Examples

• Area: For a rectangular sheet of paper, the area tells us how much space is covered by the paper.
• Surface Area: For a box, the surface area tells us how much paper is needed to wrap the entire box.

Examples Related on Area and Surface Area

Example 1: Find the area and surface area of a circular park whose radius is 9 m.

Solution:

From the formula, we know,

Area of circle = πr²

A = 22/7 × 9 × 9

A = 254.57 sq.m.

Also, we know the surface area of a sphere = 4πr²

A = 4 x 22/7 x 92 = 1018.28 sq.m.

Example 2: Find the lateral surface of a Hemi- Sphere with radius 6 cm.

Solution:

Formula of Lateral Surface Area of Hemi-Sphere = 2πr²

LSA = 2 × 3.14× r × r = 2 × 3.14 × 6 × 6

LSA = 226.08 sq.cm.

Example 3: Find the Total surface of a Cube with a side of 10 m.

Solution:

Formula of Total Surface Area of Cube = 6a²

TSA = 6 × a × a = 6 × 10 × 10

TSA = 600 sq.m.

Practice Problems on Area and Surface Area

Problem 1: Find the surface area of cylinder with base radius 14 m and height 10 m.

Problem 2: Find the surface area of cone with base radius 10 mm and height of cone is 12 mm.

Problem 3: Calculate the total surface area of a cylinder with a radius of 4 cm and a height of 10 cm.

Problem 4: A rectangle’s area is 60 square meters, and its length is 12 meters. Find the width of the rectangle.

Problem 5: A pyramid has a total surface area of 500 square meters. The base of the pyramid is a square with a side length of 10 meters. Find the slant height of the pyramid.

Things to Remember

• Area is related to a two-dimensional measurement while the surface area is related to a three-dimensional measurement.

• Area is that space that is reserved by 2-dimensional figures and the surface area is that space reserved by the external part of the 3-dimensional shape.

• Area of any shape depends on the dimensions of the shape and it may vary.

• Triangles, rectangles, circles, and squares are the best examples of Area, and cubes, cuboids, prisms, and cylinders are the main examples of surface area.

• To find the area of a plane, one needs to find the area in one shape.

• To find the surface area, one needs to sum up the area of all the faces.

• Surface area has three parts: CSA, LSA and TSA.

FAQs on Difference Between Area and Surface Area

What is the area of a shape in a flat surface?

Area of the shape in a flat surface is the region covered by that shape and which determines the size of the shape.

What is the surface area of a solid?

Surface area of a solid shape is the measurement of the exposed surface of the shape.

What is the difference between surface area and total surface area?

Surface area is the area of one face of a solid exposed in a three-dimensional plane. The total surface area is the sum of the area of all the surfaces of the solid. For example, a cube has 6 faces, so its total surface area will be 6 times the surface area of one face. Since the face of the cube is in a square shape, therefore, the total surface area will be 6 x side²

Is the area of a rectangle and cuboid same?

Area of rectangle is equal to the product of its length and breadth. Area of a cuboid is the total surface area of the cuboid which is equal to twice of

(Length × breadth + Breadth × Height + Length ×x Height)

How do area and surface area differ in their applications?

• Area: Used for two-dimensional shapes and figures, such as calculating the size of a floor, the size of a piece of land, or the amount of paint needed for a wall.
• Surface Area: Used for three-dimensional objects, such as determining the amount of material needed to cover the outside of a box or the total area of the surface of a ball.