Area Problem 3
Geometry
Level
4
In the diagram,
- the centers of the two circles are at the midpoints of adjacent sides of a regular pentagon;
- the two circles intersect at the center of the pentagon;
- the area of the pentagon is 900.
What is the total area of the red regions?
The answer is 540.
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Therefore the area of the red region is 5 3 the area of the pentagon or A r e d = 5 3 A p e n t a g o n = 5 3 × 9 0 0 = 5 4 0 .