Question

ABCDEFGHIJ is a regular decagon with a radius of 25.89 units. Find the area of ABCDEFGHIJ. Round the answer to the nearest tenth. A. 123.1 square units B. 769.4 square units C. 1,969.7 square units D. 7,878.9 square units

Answer 1

Let's call the midpoint of GF M.
MF = 16/2 = 8
KF = 25.89
MK = sqrt(25.89^2 - 8^2)
MK = 24.62
MKF = 8 * 24.62 / 2 = 98.48 square units for one triangle
There are 20 of those triangles that make up the decagon.
Therefore the total area = 20(98.48) = 1969.6 which would be option C