Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number. There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus. For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus. Area plays an important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions. Area can be defined through the use of axioms, defining it as a function of a collection of certain plane figures to the set of real numbers. It can be proved that such a function exists. (Wikipedia).
Introduction to Area and Area Formulas
This video defines area and finds the area of various shapes. http://mathispower4u.com
From playlist Perimeter and Area
What is the formula for the area of a triangle
π Learn how to find the area and perimeter of triangles. A triangle is a shape of three sides. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. The area of a triangle is given by half
From playlist Area and Perimeter
Learn how to find the area of a triangle
π Learn how to find the area and perimeter of triangles. A triangle is a shape of three sides. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. The area of a triangle is given by half
From playlist Area and Perimeter
How to determine the height of a triangle when given the area
π Learn how to find the area and perimeter of triangles. A triangle is a shape of three sides. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. The area of a triangle is given by half
From playlist Area and Perimeter
Finding the area of a triangle from a word problem
π Learn how to find the area and perimeter of triangles. A triangle is a shape of three sides. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. The area of a triangle is given by half
From playlist Area and Perimeter
Finding the length of a triangle using algebraic expression and perimeter - Online tutor
π Learn how to find the area and perimeter of triangles. A triangle is a shape of three sides. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. The area of a triangle is given by half
From playlist Area and Perimeter
How to find the area of a triangle
π Learn how to find the area and perimeter of triangles. A triangle is a shape of three sides. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. The area of a triangle is given by half
From playlist Area and Perimeter
How to determine the area of a triangle
π Learn how to find the area and perimeter of triangles. A triangle is a shape of three sides. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. The area of a triangle is given by half
From playlist Area and Perimeter
How to determine the area for a triangle
π Learn how to find the area and perimeter of triangles. A triangle is a shape of three sides. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. The area of a triangle is given by half
From playlist Area and Perimeter
ARE YOU FINDING THE RIGHT AREA?!! Area under vs. area enclosed by a graph
βΊ My Integrals course: https://www.kristakingmath.com/integrals-course Often calculus textbooks and professors will distinguish between area under the curve, or area under the graph, and the area enclosed by the curve. The area under the curve is the net area, it's the value of the integ
From playlist Integrals
Math 7: Module 3 Lessons 21 and 22 on Surface Area
From playlist Eureka Math Grade 7 Module 3
Surface Area of a Pyramid & Volume of Square Pyramids & Triangular Pyramids
This basic geometry video tutorial explains how to find the volume and surface area of a pyramid - specifically a square pyramid and a triangular pyramid. This video also provides the formula needed to calculate the lateral area of a square pyramid and a triangular pyramid. This video co
From playlist Pre-Algebra Video Playlist
Lateral Area and Surface Area of Cones, Pyramids, Cylinders & Prisms
Learn how to find the lateral area and surface area of cones, pyramids, cylinders and prisms in this video math tutorial by Mario's Math Tutoring. We discuss the formulas and how to easily memorize the formulas by grouping cylinders and prisms together and cones and pyramids together. By
From playlist Geometry
Areas of Slices and Caps, and Archimedes' Formula | Algebraic Calculus One | Wild Egg
We introduce the signed areas of slices of curve segments, obtained from chords, and areas of caps, obtained from tangents to curve segments. For the case of quadratic polynomially parametrized curves, or de Casteljau Bezier curves, we derive important formulas for these areas, and exten
From playlist Old Algebraic Calculus Videos
Velocity-Time Graphs: Area Calculations
Many Physics students become frustrated and confused once the topic of Kinematic Graphing is covered. But it doesn't need to be that way. Β This is the fourth of four videos explaining the details for understanding velocity-time graphs. This video focuses on the use of an area calculation t
From playlist Kinematics Video Tutorial Series
Calculus 1 Lecture 4.5 Part 4: The Fundamental Theorem of Calculus
From playlist Calculus 1 Playlist 1
Geometrical Snapshots from Ancient Times to Modern Times - Tom M. Apostol - 11/5/2013
The 23rd Annual Charles R. DePrima Memorial Undergraduate Mathematics Lecture by Professor Tom M. Apostol was presented on November 5, 2013, in Baxter Lecture Hall at Caltech in Pasadena, CA, USA. For more info, visit http://math.caltech.edu/events/14deprima.html Produced in association w
From playlist Research & Science
What is Calculus - Lesson 4 | Integration | Don't Memorise
In this video, we will understand the idea of integration. The basic idea of integration was known to people since ancient times, and it was called the method of exhaustion. But this method was not a general one that could be used for everything. The technique of integration is a general m
From playlist Calculus - Basics
The Cross Product and Meister's Formula b) | Algebraic Calculus One | Wild Egg
In this lecture, we continue our discussion of cross products of planar vectors and move towards a famous and useful formula of J. Meister. This is a lecture in the Algebraic Calculus One course, which will present an exciting new approach to calculus, sticking with rational numbers and
From playlist Algebraic Calculus One from Wild Egg
Find the area of an oblique triangle - Online tutor - Free Math Videos
π Learn how to find the area and perimeter of triangles. A triangle is a shape of three sides. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. The area of a triangle is given by half
From playlist Area and Perimeter