Difference Between Area and Surface Area

Area vs Surface Area

Geometry is a main branch of mathematics where we learn about shapes, size and properties of figures. It helps us understand and classify spaces.

Area

In Euclidean geometry, we talk about properties of two-dimensional figures, or in other words plane figures, such as rectangles, triangles and circles. It is most likely that the term ‘area’ comes to our mind, when we talk about plane geometry, which is also known as Euclidean geometry. Area is an expression of a size of a plane figure. A plane figure is a two-dimensional shape, which is bounded by lines called sides. The area of a plane figure is a measure of the surface covered by a given shape. Therefore, it is the amount of the surface enclosed within its bounding lines. Area is expressed in square units. There are several well-known formulas to calculate the areas of basic plane figures.

Surface Area

Simply, surface area is the area of a given surface of a solid. A solid is a three-dimensional shape. A polyhedron is a solid bounded by flat polygonal faces. Cuboids, prisms, pyramids, cone and tetrahedrons are few examples for polyhedrons. Therefore, the surface area of a polyhedron is the summation of areas of its faces. We can use the basic area formulas to generate area of a polyhedron.

For example, a cube has six faces. Therefore, its surface area will be the sum of the areas of all six surfaces. Since all the sides of a cube are squares with equal base sizes, we can express the surface area of a cube as 6 x (Area of a face of the cube (which is a square)).

Let us consider a right circular cylinder. A cylinder is bounded by two parallel planes or bases and by a surface generated by revolving a rectangle about one of its sides. The bases of a right circular cylinder are circles. Therefore, the surface area of the cylinder can be expressed as a summation of areas of two circles and a rectangle. The area of the curved surface of the cylinder, which is a rectangle is equals to (Circumference of the base) x (Altitude). Since the circumference of a circle with a radius r is 2Π r, the surface area of a cylinder with base radius r and altitude h is equals to 2Πrh + 2Πr².

Calculation of surface area for three-dimensional objects, which are bounded by surfaces that are curved in more than one direction such as the sphere would be hard than it is for polyhedron. Like area, surface area is also expressed in square units.