Answer:
b. 386.3 unit²
Step-by-step explanation:
∠AOB = 360 /5 = 72
∠BOS = 72 /2 = 36
tan ∠BOS = tan 36° = (1/2 s) / 10.3 = 0.73
S = 2 x 10.3 x 0.73 = 15.04
Area = (15.04 x 10.3 x 5) / 2 = 387.28 ≈ 386.3
Answer:
b. 386.3 unit^2.
Step-by-step explanation:
The apotherm is a line drawn from the center of the pentagon to the midpoint of one of the sides.
The area is 5 times the area of one of the triangles (drawn from the center to 2 adjacent vertices of the pentagon) whose height = the apotherm. This triangle is an isosceles triangle with base angles = 108 /2 = 54 degrees, (because the internal angles of a regular pentagon = 108 degrees).
Half of the base of the triangle is obtained using trigonometry:
tan 54 = height / 1/2 base
1/2 base = 10.3 / tan 54
= 7.483 m.
Area of the triangle = 1/2 base * height = 7.483 * 10.3 m
Area of the pentagon = 5 * 7.483 * 10.3
= 385.3 m^2
