Difference Between Area and Surface Area
by Daisy, Jul 12 2023
Introduction
Geometry focuses on the analysis of shapes and can be divided into two main categories: plane geometry and solid geometry. Plane geometry is concerned with two-dimensional figures such as squares, circles, rectangles, triangles, and many other shapes. On the other hand, solid geometry is centred around the examination of three-dimensional shapes like cubes, cuboids, cylinders, cones, spheres, and more.
Studying these shapes enables us to determine various aspects such as lengths, widths, area, surface area, volume, perimeter, and other terms.
Students often find it difficult to differentiate between the concepts of area and surface area, even though they appear similar but represent distinct ideas.
Area is a two-dimensional measurement, while surface area is a three-dimensional measurement. This article will delve into the definitions of area and surface area, highlighting the differences between these two concepts.
What is the Area
Area is the measurement of the size or extent of a two-dimensional shape or figure, such as polygons and circles. It quantifies the amount of space enclosed within the boundaries of the shape and is usually measured in square units like square metres or square feet. Different shapes have different formulas to calculate the area.
Example:
For a rectangle, the area is calculated by multiplying its length and width (Area = length × width).
If you have a rectangle with a length of 4 metres and a width of 3 metres, its area would be 12 square metres.
What is the Surface Area
Surface area is a measurement that represents the total area that the surface of a three-dimensional object, like a cube, sphere, or cylinder, occupies. It measures the combined area of all the faces or surfaces of the object and is expressed in square units.
Example:
For a cube, the surface area is calculated by finding the area of one face (side length squared) and then multiplying it by the number of faces (6).
So, the surface area of a cube is 6s², where s is the side length. If you have a cube with a side length of 2 metres, its surface area would be 24 square metres.
Differences between Area and Surface Area
Area and surface area are both measurements of shapes; however, they differ in their dimensionality and application.
- Dimensionality: Area is related to two-dimensional shapes such as squares, circles, rectangles, and triangles. It measures the extent of a flat, two-dimensional surface within these shapes. Surface area, on the other hand, pertains to three-dimensional shapes like cubes, cylinders, or spheres. It measures the combined area of all the faces, including curved surfaces, of a three-dimensional object.
- Application: Area is commonly used for measuring flat surfaces such as floors, walls, or pieces of land. Surface area is generally utilized when dealing with three-dimensional objects, for instance, determining the amount of paint required to cover a container or the outer surface area of a building.
In summary, area is a two-dimensional measurement applied to flat shapes, while surface area is a three-dimensional measurement used for analyzing three-dimensional objects.
Summary
Area is a two-dimensional measurement used to quantify the size or extent of a flat shape like rectangles or circles, while surface area is a three-dimensional measurement representing the total area occupied by the surface of a 3D object like cubes or spheres.
Their main differences lie in dimensionality and application. Area applies to 2D shapes and is used for measuring flat surfaces, while surface area pertains to 3D shapes and is used when analyzing three-dimensional objects.