# 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?

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

Locate the Center of Diameter label it F. Draw the square AFEG. Shade the figure like shown below.

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:

Solving for Area of triangle AFE:

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

Area of shaded region=

Solving for area of leaf:

Area of leaf = 8(Area of shaded region)

Area of leaf =

Area of leaf =

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### Dan

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