Geometry

Regular Polygons

Regular Polygons - Decomposition into Triangles

         

Consider a rectangle with diagonals as shown in the above diagram. If the area of BCE\triangle BCE is 32,32, what is the area of ABE?\triangle ABE?

The above diagram is a regular pentagram. Let TRS\lvert\triangle TRS\rvert denote the area of TRS,\triangle TRS, and PQRS\lvert\square PQRS\rvert the area of PQRS.\square PQRS. If ABC=52,\lvert\triangle ABC\rvert=52, what is the area of the shaded region PQRSTRS?\lvert\square PQRS\rvert - \lvert\triangle TRS\rvert?

In the above diagram, ABCD\square ABCD is a square and DE\overline{DE} is perpendicular to one of its diagonals AC.\overline{AC}. If the length of DE\overline{DE} is 21.21. what is the length of AC?\overline{AC}?

In the above diagram, figure ABCDEABCDE is a regular pentagon centered at point FF. Find the area of quadrilateral CDEFCDEF when the area of triangle ABFABF is 56.56.

In ABC\triangle ABC above, L,ML,M and NN are the midpoints of AB,BC\overline {AB}, \overline {BC} and AC,\overline {AC}, respectively. If the area of LMN\triangle LMN is 54,54, what is the area of ABC?\triangle ABC?

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