Introduction
Geometry is one of the most important aspects of mathematical concepts. Structures and their attributes make up the majority of geometry. If a student enjoys drawing figures, then Geometry is the course for him or her. However, among the students, the question emerged, "Why do we practice Geometry?" And the solution is to uncover the patterns, determining volumes, lengths, areas, and angles. However, some students get the terms area and surface area mixed up. As a result, use this article to learn the definitions of area and surface area, as well as to explore the differences between the two. The analysis of patterns is known as geometry. There are two forms of geometry: plane geometry and solid geometry. Solid geometry studies three-dimensional shapes such as the cube, cuboid, cylinder, cone, sphere, and many others. Plane geometry studies two-dimensional forms such as squares, circles, rectangles, triangles, and many others.
Surface Area vs Area
This shape must be studied in order to determine lengths, widths, area, surface area, volume, perimeter, and a variety of other terms. The phrases area and surface area are frequently misunderstood by students. They may appear to be similar, yet they are two distinct concepts. The surface area is a three-dimensional statistic, whereas the area is two-dimensional. Let's take a closer look at the descriptions of area and surface area, as well as the differences between the two in this article.
Differences Between Area and Surface area in Tabular Form
Pointers | Area | Surface Area |
Definition | Any two-dimensional geometric shape's area is the measurement of the space it takes up. Any shape's area is determined by its dimensions. | The surface area of a three-dimensional object is the calculated area. The surface area of a three-dimensional object is equivalent to the total of the areas of all the subject's 2D faces. |
Unit of Measurement | It is measured in Square Units | It is also measured in Square Units. |
Area of work | It's the area taken up by a shape's lines. | It refers to the exterior of a body rather than the interior space. |
Sides included | Knowing the sides of any 2D form allows us to determine its area. | We can compute the surface area of any form if we know all of its sides. |
Shapes effective on | The area of a 2-D figure is the measurement of its size. | The size of a 3-D figure is measured by its surface area. |
Examples of shapes | Circle, Square, Rectangle, Triangle, Trapezium, etc. | Sphere, Cuboid, Pyramid, Cone, Trapezoid. |
What is Area?
Definition: The total space filled by two-dimensional items or flat shapes is specified as the area. In other terms, a figure's area is defined as the number of square units that cover the closed figure's surface.
Unit of Measurement: It is specified in square units, which is a unit of measurement. Because only length and breadth can be measured for 2-dimensional forms, the area only has length and width.
Eligible shapes: Circle, Rectangle, Square, Rhombus, Parallelogram, Triangle, Quadrilateral, Trapezium.
Area of a Circle
A circle's area is the amount of space it takes up in a two-dimensional plane. The area of a circle, on the other hand, is the space occupied within the demarcation of a circle.
Formula: A = πr^{2} [where, A=area of the circle, r=radius of the circle, π (Pi) =3.14(approximately) or 22/7]
Area of a Square
The number of square units required to fill a square is known as its area. To put it another way, we consider the length of a square's side when calculating its area. The area of a square equals the product of its two sides because both of its sides are equal. Square meters, square feet, square inch, and square cm are popular units for measuring the area of a square.
Formula: Area of a square = Side × Side = S^{2}
Area of a Rectangle
The number of unit squares within the rectangle's edge determines its area. The area of a rectangle, on the other hand, is the space occupied within the rectangle's perimeter. The unit length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles on the floor, you can quickly determine how much space it takes up. This will also assist you in determining the rectangle floor's area.
Formula: Area of a Rectangle = (Length × Breadth) square units
Area of a Rhombus
The area of a rhombus in a two-dimensional space can be described as the amount of space enclosed by a rhombus. It is measured in square units and indicates the overall amount of unit squares that can fit into it. The opposite sides of a rhombus are parallel, the opposite angles are equal, and the neighboring angles are supplementary.
Formula:
- Area of a Rhombus = base × height square units
- Area of a Rhombus = 1/2 × diagonal 1 × diagonal 2 square units
Area of a Parallelogram
The region of a parallelogram inside a two-dimensional plane is the overall area by a parallelogram. A parallelogram is a two-dimensional figure of four sidewalls in geometry. It's a quadrilateral with equivalent and concurrent opposite sides. The area of a parallelogram is the space bounded by its four edges. The area of a parallelogram is directly proportional to the product of its lengths.
Formula:
- Area of a parallelogram= base × height square units
- Area of a parallelogram= 1/2 × diagonal 1 × diagonal 2 square units
Area of a Triangle
The area of a triangle is the area enclosed by the triangle's sides. The area of a triangle changes depending on the length of the sides and the internal angles of the triangle. A triangle's area is measured in square units.
Formula: Area of triangle = 1/2 × base × height
Area of a Trapezium
The area of a trapezium in a two-dimensional plane is the area covered by a trapezium. It's the 2D space that's measured in square units. A trapezium is a two-dimensional shape that belongs to the quadrilateral family. It has its own properties and calculations based on area and perimeter, just as other geometrical shapes.
Formula: Area of a trapezium= (1/2) h (a+b) [a and b are the length of parallel sides/bases of the trapezium; h is the height or distance between parallel sides.]
What is Surface Area?
Definition: The total area of all the faces of a three-dimensional object is its surface area. We employ the concept of surface areas of different items in real life when we want to envelop something, decorate something, and subsequently build something to obtain the greatest design possible. Varying 3D shapes have different surface areas in geometry, which may readily be determined using the formulas we'll learn in this lesson.
Unit of measurement: Solids' surface area is quantified in square units. For example, if the dimensions are in meters (m), the surface area will be in m^{2}, which is the International System of Units' standard unit of surface area (SI).
Eligible shapes: Sphere, Cuboid, Pyramid, Cone, Trapezoid.
Types of Surface Area
- Total surface area: The total surface area includes the base(s) as well as the curving component. It is the whole area covered by the object's surface. The total area of a shape with a curved surface and base is equal to the sum of the two areas.
- Lateral surface area: The area of all the faces other than the bottom and top faces or bases is known as the lateral surface area.
- Curved surface area: The area of only the curved part of a shape, excluding base, is referred to as curved surface area (s). For shapes like a cylinder, it's also known as lateral surface area.
Surface area of a Sphere
The area covered by a sphere's outer surface in three-dimensional space is known as its surface area. A sphere, like a circle, is a three-dimensional solid with a round shape. A sphere differs from a circle in that a circle is a two-dimensional figure or a flat shape, while a sphere is a three-dimensional shape. As a result, the area of a circle differs from the area of a sphere.
Formula: Surface area of a sphere= 4πr^{2} square units
Surface area of a Cuboid
The total surface covered by all six faces of the cube is known as the cube's surface area. Calculating the area of the two bases and the area of the four lateral sides yields the total surface area of a cube. A cube is a solid three-dimensional shape made up of square faces. In cases when we want to wrap a cube, paint the cube's surfaces, and so on, knowing the surface area is crucial.
Formula: Surface Area of a Cube = (6 × side^{2}) square units
Surface area of a Pyramid
A pyramid's surface area is calculated by adding the areas of all its faces. A pyramid is a three-dimensional form with a polygonal base and triangle-shaped side faces that meet at a point called the apex (or vertex). The altitude or height of the pyramid is the perpendicular distance between the apex and the center of the base. The 'slant height' is the length of the perpendicular drawn from the apex to the base of a triangle (side face).
Formula:
- Square pyramid= 2 x b × s + b^{2 }[ b= side of the base; s= slant height]
- Triangular pyramid= 1⁄2(a × b) + 3⁄2(b × s) [a= side height of base; b=side of the base; s= slant height]
Surface area of a Cone
The surface of a cone is the area occupied by the cone's surface layer. It is always conveyed as a square unit. A cone is formed by layering many triangles and twisting them around an axis. Because it has a stable bottom, it has a total surface area as well as a curved surface area. A cone is categorized as either right circular or oblique. The centroid of a right circular cone is customarily vertically above the center of the base, while the node of an oblique cone is not upright above the bottom of the specimen.
Formula: Surface area of cone= πr {√(h2 + r2)}. [h=height of the cone; r=radius of the base]
Area of a Trapezoid
The surface area of a trapezoidal prism is the area occupied by the surface of a trapezoidal prism. We can say that the trapezoidal prism has a total surface area and a curved surface area because it has a flat base. Any three-dimensional geometrical shape's surface area is equal to the total of the surfaces of that contained solid, which equals the areas of all the faces. Two trapezoidal faces and four rectangular faces make up a trapezoidal prism. The area of the base, the perimeter of the base, and the slant height of any side of the prism make up the easy formula for computing the surface area of a trapezoidal prism.
Formula: Surface area of a Trapezoid= (b1+b2)h + PH [b1,b2= bases of the trapezoid; P= perimeter of the trapezoid; H= Height of the trapezoid]
Differences between Area and Surface Area in Points
- Surface area is linked to a three-dimensional shape, whereas area is linked to a two-dimensional contour.
- Any planar two-dimensional shape's area is the territory or region it occupies. The area or space occupied by the lateral surface and the area of all the faces of a three-dimensional shape is known as surface area.
- Area is calculated using only two dimensions or variables. The area of a rectangle, for illustration, is computed by multiplying its length and width. Surface area is calculated using three dimensions or values. The surface area of a cuboid, for instance, is computed by multiplying its length, breadth, and height.
- The area is used to evaluate the space or region to be painted on a board or the overall space represented by a flat piece of land in real life. The surface area is used in real life to determine the cost of roofing a cuboid-shaped box or painting the surface of a simple cubic box.
Conclusion
Mathematics has a way of making us think, rethink, and think again. People can get confused with explanations, particularly with similar terms, as if mathematics isn't difficult enough with its formulae, operations, and etymology. Most of us are aware that geometry is the science of measuring the earth, space, structure, and figures, and that when one thinks of geometry, the phrase 'area' comes to mind. When it comes to 2-dimensional surfaces, the phrases "area" and "surface area" are frequently interchanged. However, it is more ideally employed to indicate the size of a 3-dimensional surface revealed by a given solid.