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Home > CCG > Chapter 12 > Lesson 12.2.3 > Problem 12-86

12-86.

Find the area of the shaded region of the regular pentagon at right. Show all work.

A pentagon with the vertices labeled B, C, M, A, and N starting at the lower left vertex and going counter clockwise. B, C, is 4. Two diagonals are drawn: B, A, and C, A. The triangle A, B, C, is shaded.

Label the shaded region as ΔABC.

The measure of each angle in a pentagon is equal to .

Therefore, the measure of  is equal to 

Divide into two triangles. Use a trigonometric ratio to solve for .

units

A pentagon with the vertices labeled B, C, M, A, and N starting at the lower left vertex and going counter clockwise. B, C, is 4. Two diagonals are drawn: B, A, and C, A. The triangle A, B, C, is shaded.

    From the vertex, A, is dropped a line perpendicular to the base, B, C, at point, D, dividing the base into 2, 2 unit segments. Right triangles A, B, D and A, D, C are created.