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An ellipse (English: Ellipse) is a flat curve, formed by cutting a circle such that for every point on the curve, the total distance to two focal points is constant.
An ellipse resembles an egg shape and is widely applied in mathematics, physics, and engineering. Calculating the area of an ellipse in CAD, especially in architectural construction like the Roman Colosseum, Ellipse Tower in Hanoi...
II. Formula for calculating the area of an ellipse and illustrative examples
1. Formula for calculating ellipse area
A circle is a special case of an ellipse, formed when the two focal points coincide. If the formula for calculating the area of a circle is π.r.r (π x r x r), then the formula for calculating the area of an ellipse is A = π.a.b.
Where:
- a is the length of the major semi-axis.
- b is the length of the minor semi-axis.
- π (mathematical constant) = 3.14159265359.
Thus, in 2-dimensional space geometry, an ellipse appears as a stretched and elongated circle. To calculate the area of an ellipse, you only need to know the lengths of the major and minor axes.
Example of calculating the area of an ellipse: Given an ellipse with two symmetrical axes A1A2, B1B2. Where, the major axis A1A2 = 10 cm; the minor axis B1B2 = 6 cm. What is the area of this ellipse?
We have:
- A1, A2, B1, B2 are the vertices of the ellipse.
- A1A2 is the major axis (2a) => a = 5 cm.
- B1B2 is the minor axis (2b) => b = 3 cm
Applying the formula for calculating the area of an ellipse yields A = π x 5 x 3 = 15π cm² (approximately 47 cm²).
In addition to memorizing the formula for calculating the perimeter and area of an ellipse as described above, students can also rely on various apps, online math solving websites to compute, find, compare answers to problems involving ellipse perimeter, area, and equations.
2. Equation of an Ellipse
The general equation of an ellipse is:
Example of an ellipse equation:
3. Components and Shape of an Ellipse
From the equation, you can determine the lengths of the axes, coordinates of the focal points, coordinates of the vertices of that ellipse. Specifically as follows:
4. Application of Formula for Calculating the Area of an Ellipse in Mathematics
Here are 2 specific examples to deepen your understanding of the ellipse formula & its application in daily life.
With the article how to calculate the area of an ellipse shared by Mytour, it is hoped that students will grasp the theoretical knowledge & apply it proficiently in their studies.
https://Mytour.vn/cach-tinh-dien-tich-hinh-elip-32063n.aspx
Furthermore, to study well and achieve high scores in Geometry, students can also explore formulas for calculating the area of a square, rhombus area calculation, parallelogram area calculation. Best wishes to all students.
