by
Tashia J. Hansen

Table of Contents

In geometry, a form is defined as the boundary figure. A combination of lines, points, and curves will create the boundary. There are two different geometric forms, for example:

• Two Dimensional – Dynamic forms

• Three Dimensional – Size Forms

All shapes can be measured in different measurements such as **surface area**, volume, surface area, perimeter, etc. In this article, let us talk about formulas for 2D figures and 3D figures.

It is a quantity that shows the extent of a two-dimensional figure or shape in the plane. Lamina shapes include 2D figures drawn on a plane, e.g., circle, square, triangle, rectangle, trapezium, rhombus, and parallelogram. The region occupied by them in space includes forms such as the cycle, triangle, square, rectangle, parallelogram, etc.

The shape of a polygon: a polygon is a two-dimensional form made up of straight lines. Triangle, hexagon, and pentagon are examples of polygons. The names of the forms describe the number of sides in the form. For example, a 3-sided triangle and a 4-sided rectangle. Therefore, any shape formed with three straight lines is known as a triangle, and any form drawn by connecting four lines is known as a quadrilateral. It is the region within the border/perimeter of the forms to be taken into account.

• A surface such as the surface of a sphere may be flat or curved

• A two-dimensional surface is always because it’s about width and length only. When there is a height, it’s the third dimension, that’s a room.”

One speaks about surfaces in mathematics, especially geometry. You are taught how to compute the area in mathematics class.

The two-dimensional shapes (2D shapes) are also known as flat shapes; do the shapes have two dimensions only. It has length and breadth. The thickness doesn’t exist. The area and perimeter are the two different measurements used to measure the flatforms. The forms that can be drawn upon the piece of paper are two-dimensional forms. Some 2D shapes are square, rectangular, circular, triangle, etc.

Their forms can usually be determined by the amount of paint needed for a single covering of the surface. Following are how the area is calculated according to the number of sides in the form, as shown in the figure below.

**How to calculate the area of a circle?****Can you****calculate the area of the triangle?****How to calculate the area of the square?****What way****to calculate the area of the rectangle?****How to calculate the area of the parallelogram?****Do you****calculate the area of trapezium?****How to calculate the area of an ellipse?**

**Here are the answers to these questions and formulas for all the different types of shapes in a tabular form are given:**

Shape | Area | Terms |

Circle | π × r^{2} | r = radius of the circle |

Triangle | ½ × b × h | b = base = height |

Square | a^{2} | a = length of the side |

Rectangle | l × w | l = length = width |

Parallelogram | b × h | b=baseh=vertical height |

Trapezium | ½(a+b) × h | a=lenght b=lenght of parallel sides = height |

Ellipse | πab | a = ½ minor axis = ½ major axis |

3D forms, called solid forms, are three-dimensional forms known as length, width, and thickness. The volume and surface area are two distinct actions to define the three-dimensional forms. The three-dimensional forms are generally derived from a two-dimensional rotation. Therefore, a 2D form should be the surface of every 2D form. Accordingly, if the surface area of solid forms is to be calculated, we can calculate easily from the size of the 2D forms.

According to the International System of Units (SI), the standard unit of area is the square meter (written as m 2), according to the International System of Units (SI), and is the surface of one square meter of sides. For example, a particular form with 3 m2 would have the same area as three squares of this type. The solid object surface is a measure of the overall area of the object’s surface.

It is updated to the surface area of form for 3D / solid forms such as cube, cuboid, sphere, cylinder, and cones. In the table, here are the formulas for three-dimensional shapes:

**How to calculate the surface area of a cube?****Can you****measure the surface area of a rectangular prism?****How to calculate the surface area of the cylinder?****Do you calculate the surface area of the cone?****How to measure the surface area of a sphere?****How we can measure the surface area of the hemisphere?**

**The answers **to **the following questions are given in the tabular form:**

Shape | Surface area | Terms |

Cube | 6a^{2} | a = length of the edge |

Rectangular prism | 2(wl+hl+hw) | l = length = width = height |

Cylinder | 2πr(r + h) | r = radius of the circular base = height of the cylinder |

Cone | πr(r + l) | r = radius of the circular base = slant height |

Sphere | 4πr^{2} | r = radius of the sphere |

Hemisphere | 3πr^{2} | r = radius of the hemisphere |

A further variable, i.e., height or radius, is used to **calculate the surface area** of the shapes and the planar form areas.

Take a radius r circle and make endless concentration circles. Now create a line segment equal to the radius from the center to the border, and cut the figure along with this segment. The triangle with the base equal to the circle’s circumference will be formed, and the height equals the ray of the external circle, i.e., r. It can therefore be calculated as 1⁄2 * height basis *, i.e., 1⁄2 * 2μr*r

You may get more about circumference and calculate the circumference of a circle

The main difference of area to the perimeter is that the region occupied by form and the length of the external shape border is defined by the perimeter. Thus, both parameters define the size of a form. Find out more about the area and perimeter here.

Both areas & limits seem to be important in geometry in the field of mathematics. Unfortunately, these words can easily be confused, which look similar but have a big difference. Here we will discuss the fundamental differences and **calculate the area **& perimeter for those forms with some basic features.

** The area** is defined as a two-dimensional flat object-occupied area/area. The square units are measured.

Consider a square that has a side, then a2 is given for the area of the square.

**Perimeter** is the limited length of a closed figure. The perimeter will then be the total of the four sides of the square, for example, a side length equal to ‘a’, i.e. ‘4a.’ The unit is used for measuring the perimeter.

Area | Perimeter |

The region occupied by a closed shape in a two-dimensional plane is known as area. | It is known as the length of the outer boundary of a closed shape |

It is measured in square units | It is measured in units |

Example: Area of a plot for farming | Example: Fencing the agricultural plot |

Area of square = side^{2} | Perimeter of square = 4 x side |

Area of a rectangle = Length × Breadth | Perimeter of rectangle = 2(Length+Breadth) |

Area of triangle = ½ × base × height | The perimeter of triangle = Sum of all three sides |

Area of rhombus = ½ (product of diagonals) | The perimeter of rhombus = 4 × side |

Area of trapezium = ½ (sum of parallel sides) | The perimeter of trapezium = sum of all sides |