Areas. Area calculation for geometric figures
The online area calculation simulations on this page will help you discover unexpected relationships of areas to other mathematical concepts. We will discover different methods for area calculation for geometric figures. The versatility of area calculus makes it an indispensable tool for solving real problems and modeling complex situations.
This Thematic Unit is part of our Mathematics collection
STEM OnLine mini dictionary
Area
Magnitude that measures the extent of a two-dimensional surface; its standard SI unit is the square meter (m²) and in the imperial system the square foot (ft²).
Area Calculation
Mathematical process to determine the measurement of a surface using geometric formulas or integration.
Distance
Spatial interval measurement between two points; its standard SI unit is the meter (m) and in the imperial system the foot (ft).
Geometric Formula
Mathematical expression that establishes the relationship between a figure’s dimensions to determine its area.
Height
The perpendicular distance measured from the base to the furthest point or vertex of a figure.
Surface
The outer extent of a body or figure that possesses only two dimensions (length and width). its standard SI unit is the square meter (m²) and in the imperial system the square foot (ft²).
What is area calculation for geometric figures?
The area calculation for geometric figures in mathematics refers to the process of determining the size or measure of a two-dimensional region of the plane. There are different methods and techniques for calculating areas, depending on the shape and characteristics of the region in question.
Methods for area calculation
Some of the most common methods are described below:
Areas of simple geometric figures
For simple geometric figures, such as triangles, rectangles, squares and circles, there are specific formulas to calculate their areas. For example, the area of a triangle can be calculated by multiplying the base by the height and dividing the result by two, while the area of a circle can be obtained using the formula πr^2, where r is the radius.
Areas of compound geometric figures
For more complex figures, one can use techniques of decomposition into simpler figures and then add or subtract the corresponding areas. For example, the area of a trapezoid can be calculated by adding the area of two triangles and a rectangle.
Integration
Integral calculus is used to calculate areas of more irregular regions or curves. If a function describing the curve bounding the region is known, the area can be calculated using the definite integral of that function over a given interval. This involves dividing the region into infinite vertical strips, calculating the area of each strip, and then summing all the areas.
Green’s Theorem
For regions of the plane bounded by simple closed curves, Green’s theorem provides a relationship between the enclosed area and a line integral over the curve. This theorem states that the area enclosed by the curve is equal to the line integral of a specific vector function over the curve.
These are just some of the main methods for calculating areas in mathematics. Each of them is applied according to the characteristics of the region in question and the availability of information about it.
STEM OnLine mini dictionary
Area
Magnitude that measures the extent of a two-dimensional surface; its standard SI unit is the square meter (m²) and in the imperial system the square foot (ft²).
Area Calculation
Mathematical process to determine the measurement of a surface using geometric formulas or integration.
Distance
Spatial interval measurement between two points; its standard SI unit is the meter (m) and in the imperial system the foot (ft).
Geometric Formula
Mathematical expression that establishes the relationship between a figure’s dimensions to determine its area.
Height
The perpendicular distance measured from the base to the furthest point or vertex of a figure.
Surface
The outer extent of a body or figure that possesses only two dimensions (length and width). its standard SI unit is the square meter (m²) and in the imperial system the square foot (ft²).
Explore the exciting STEM world with our free, online, simulations and accompanying companion courses! With them you’ll be able to experience and learn hands-on. Take this opportunity to immerse yourself in virtual experiences while advancing your education – awaken your scientific curiosity and discover all that the STEM world has to offer!
Area builder
Create with this simulation your own shape with colored blocks and explore the relationship between perimeter and area. Compare the area and perimeter of two shapes side by side. Test yourself on the game screen to build shapes or find the area of funky shapes – try to collect lots of stars!
Method of the sum of rectangles
With this simulation you can see how the sum of rectangles is used to calculate geometric areas. Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying algebraic expressions. Use the “Game” window to test your multiplication and factoring skills.
Giants of science
“If I have seen further, it is by standing on the shoulders of giants”
Isaac Newton
Euclides
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Become a giant
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Giants of science
“If I have seen further, it is by standing on the shoulders of giants”
Isaac Newton
Euclides
–
Evangelista Torricelli
–
Become a giant
计算几何 | Computational Geometry
Introduction to Geometry
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Test your knowledge
What does it mean to calculate the area of a figure?
How is the area of basic geometric figures calculated?
What if the figure is irregular—how can the area be calculated?
Why do some area formulas seem strange or different for each figure?
What if I don’t have all the measurements—can I still calculate the area?
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