Area
Area is the amount of space a two dimensional (flat) surface takes up. It is useful because it is how much of a material is needed to make a hollow container. Area is the amount of surface covered by a close object or shape.
Some units used to measure area are square foot, square mile, square metre and square kilometre. The area of a planar figure is often written as [math]\displaystyle{ A }[/math].[1] Areas of regular shapes such as square, rectangle, triangle and circle can be calculated through formulas.[2] The area of an irregular shape can be approximated through grid or graph paper.[3]
One can use different formulas to find the area of different shapes. For example:[2]
- Area of a rectangle is the length of any two touching sides multiplied together. In other words, length times width.
- Area of a triangle is half of the base multiplied by the perpendicular height. In other words, [math]\displaystyle{ A = \tfrac{1}{2} bh }[/math].
- Area of a circle: [math]\displaystyle{ A = \pi r^2 }[/math]
The area of a flat object is related to the surface area and volume of a three-dimensional object.
The area under a curve can be found using integration, a concept from calculus.
Area Media
A square metre quadrat made of PVC pipe
Although there are 10 mm in 1 cm, there are 100 mm2 in 1 cm2.
The area of this rectangle is lw.
A parallelogram can be cut up and re-arranged to form a rectangle.
A parallelogram split into two equal triangles
A circle can be divided into sectors which rearrange to form an approximate parallelogram.
Archimedes showed that the surface area of a sphere is exactly four times the area of a flat disk of the same radius, and the volume enclosed by the sphere is exactly 2/3 of the volume of a cylinder of the same height and radius.
Triangle area A=\tfrac{b\cdot h}{2}
Integration can be thought of as measuring the area under a curve, defined by f(x), between two points (here a and b).
The area between two graphs can be evaluated by calculating the difference between the integrals of the two functions
Related pages
References
- ↑ "List of Geometry and Trigonometry Symbols". Math Vault. 2020-04-17. Retrieved 2020-09-24.
- ↑ 2.0 2.1 "Area - Math Open Reference". www.mathopenref.com. Retrieved 2020-09-24.
- ↑ "What is Area?". www.mathsisfun.com. Retrieved 2020-09-24.