Geometry Basics: Length, Perimeter, and Area

Study Notes

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.

Description

Learn the fundamental concepts of geometry, including the formulas to calculate the length, perimeter, and area of different shapes such as rectangles, triangles, and circles. Understand the importance of these concepts in describing the size and shape of 2D objects.