The picture shows a regular pentagon ABCDE. Find the ratio of the area of triangle ABD to the area of pentagon ABCDE.
+128408 Let the side of the pentagon = S
Area of pentagon ≈ 1.72 S^2
Height of triangle
tan 72° = H / (1/2 S)
H = S tan 72° / ( 2)
Area of triangle = (1/2) S * ( S tan 72°) / ( 2) = S^2 tan 72°/4
Ratio area of triangle to area of pentagon = (tan (72°) / 4 ) / 1.72 =
tan (72°) / ( 4 * 1.72) ≈ .447
