Geometry Basics: Length, Perimeter, and Area

Length, Perimeter, and Area

Length, perimeter, and area are fundamental concepts in geometry. They provide important information about the size and shape of two-dimensional objects. This article will discuss these concepts for rectangles, triangles, circles, and surface area.

Rectangles

A rectangle is a quadrilateral with opposite sides parallel and equal in length. The length and width of a rectangle are the measurements of its sides.

Area

The area of a rectangle is calculated by multiplying its length by its width:

Area = Length × Width

Perimeter

The perimeter of a rectangle is the total distance around its boundary. It is calculated by adding the lengths of all sides:

Perimeter = 2(Length + Width)

Triangles

A triangle is a three-sided polygon. It has three sides and three angles.

Area

The area of a triangle is half the product of its base and height:

Area = 1/2 × Base × Height

Perimeter

The perimeter of a triangle is the sum of the lengths of its sides:

Perimeter = Base + Height + Side-Length

Circles

A circle is a set of points in a plane that are all the same distance from a fixed point, called the center.

Area

The area of a circle is proportional to the square of its radius:

Area = πr²

Perimeter

The perimeter of a circle is the distance around its circumference:

Perimeter = 2πr

Surface Area

Surface area is the measure of the total area of the surface of an object. It is calculated differently for different shapes.

Rectangle

The surface area of a rectangle is the product of its length and width:

Surface Area = Length × Width

Triangle

The surface area of a triangle is half the product of its sides and the semi-perimeter (the average of the side lengths):

Surface Area = 1/2 × Side-Length₁ × Side-Length₂ × (Side-Length₁ + Side-Length₂ + Side-Length₃)

Circle

The surface area of a circle is the square of its radius times π:

Surface Area = πr²

In conclusion, length, perimeter, and area are essential concepts in geometry. They provide valuable information about the size and shape of two-dimensional objects, and the formulas for these measurements vary depending on the shape of the object.