Irregular Cone Geometry Problem: Finding the Area of an Elliptical Base

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To find the area of the base of an elliptical cone using the length from the center to the vertex and the angle of the sides, one can utilize the formula A=πab, where a and b are the semi-major and semi-minor axes. The discussion suggests employing trigonometry to derive these axes by dropping a perpendicular from the vertex to the base, creating a right triangle. A helpful approach involves slicing the cone to obtain a circular cross-section, which can simplify the calculations. Despite initial challenges in geometry guides, applying these methods may lead to a solution. Understanding the relationship between the cone's dimensions and the elliptical base is crucial for solving the problem.
Appity
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Homework Statement



I'm wondering whether or not it is possible to get the area of the base of an elliptical, non-right cone if the following two parameters are known:

- length from center of ellipse up to vertex
- angle that the sides make

Here is a simple visual: http://i.imgur.com/M6jT5.png

Homework Equations



A=\pi ab

The Attempt at a Solution



I've tried looking at geometry guides with no success. I'm thinking I might be able to use some clever trig and drop a right angle down from the vertex in order to get the length of the semi-minor/major axis, but I can't reason it out. any advice would be appreciated.
 
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Hi Appity! :smile:

Hint: slice the cone so that you get a circular cross-section, then use trig to find the area of the projection. :wink:
 

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