Area of a Leaf

This post is to outline step by step solution on how to find the area of the leaf made by intersecting semicircles. This is a classical geometry problem. It might be easy for some but if this is your first time to see this problem, I doubt if you can solve it for 3 minutes.

In the figure, a leaf is made by intersecting 4 semicircles with radius 1.What is the area of  the leaf made? leaf2

[toggle title=”Solution:”]

Label the figure accordingly and locate the point of intersection of the semicircles.

leaf 3


Locate the Center of Diameter \overline{AD} label it F. Draw the square AFEG. Shade the figure like shown below.


leaf 7


Shade this part of the figure. The area of the leaf is 8 times of the area of the shaded region.

Area of shaded region = Area of Quarter Circle AFE – Area of triangle AFE

Solving area of Area of Quarter Circle AFE:

A=\displaystyle\frac{1}{4}\pi(r^2)=\displaystyle\frac{1}{4}\pi (1)=\displaystyle\frac{\pi}{4}

Solving for Area of triangle AFE:

A=\displaystyle\frac{1}{2}bh =\displaystyle\frac{1}{2}(1)(1)=\displaystyle\frac{1}{2}

Area of shaded region= Area of Quarter Circle AFE – Area of triangle AFE

Area of shaded region=\displaystyle\frac{\pi}{4}-\displaystyle\frac{1}{2}

Solving for area of leaf:

Area of leaf = 8(Area of shaded region)

Area of leaf =8(\displaystyle\frac{\pi}{4}-\displaystyle\frac{1}{2})

Area of leaf =2\pi -4


Got a problem to feature here? Send the problem and solution in the form below. Make sure to include your email.






Blogger and a Math enthusiast. Has no interest in Mathematics until MMC came. Aside from doing math, he also loves to travel and watch movies.

Latest posts by Dan (see all)

You may also like...

5 Responses

  1. Andre says:

    It’s in reality a great and helpful piece of information. I’m glad that you shared this useful info with us. Please stay us up to date like this. Thanks for sharing.

  2. I’m not sure exactly why but this site is loading extremely slow for me. Is anyone else having this issue or is it a problem on my end? I’ll check back later and see if the problem still exists.

  3. Excellent publish from specialist also it will probably be a fantastic know how to me and thanks really much for posting this helpful data with us all.

  4. Malik Mas says:

    Thank you of this blog. That’s all I’m able to say. You undoubtedly have made this web web site into an item thats attention opening in addition to critical. You certainly know a fantastic deal of about the niche, youve covered a multitude of bases. Fantastic stuff from this the main internet. All more than again, thank you for the blog.

  5. I am curious to locate out what blog system you’re utilizing? Im having some small security problems with my latest site and Id like to find something a lot more risk-free. Do you’ve any suggestions? Hmm it looks like your weblog ate my initial comment (it was super long) so I guess Ill just sum it up what I wrote and say, Im thoroughly enjoying your weblog. I too am an aspiring weblog blogger but Im still new to everything. Do you’ve any guidelines and hints for rookie weblog writers? Id definitely appreciate it.

Leave a Reply

Your email address will not be published. Required fields are marked *