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Find the area of a four leaf rose
Solution:
To illustrate the problem, it is better to draw or sketch the figure as follows
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| Photo by Math Principles in Everyday Life |
In this problem, we will get the area of one leaf and then multiply it by 4 later because the four leaves are symmetrical or identical to each other. Since the limits for one leaf are not given, then we have to solve these first as follows
set r = 0, we have
Since we have the limits for one leaf of a four leaf rose, we can further label the figure as follows
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| Photo by Math Principles in Everyday Life |
The area of the sector is given by the formula
Integrate on both sides of the equation to get the area of one leaf, we have
Since one leaf is also symmetrical, then we can rewrite the above equation as follows
Therefore, the area of a four leaf rose is
