Final answer:
An isosceles triangle with a base of 22 cm and a vertex angle of 36˚ has a perimeter of approximately 99.734 cm.
Step-by-step explanation:
An isosceles triangle has two equal sides and two equal angles. Since the triangle has a vertex angle of 36˚, the other two angles must each be (180˚ - 36˚) / 2 = 72˚. The perimeter of the triangle is the sum of the lengths of all three sides, which can be calculated as:
Perimeter = 22 cm + 22 cm + 2 * (side length of triangle)
We can use trigonometry to find the side length of the triangle. In a right triangle formed by the base and one of the legs of the triangle, with the vertex angle as the right angle, the side length can be calculated as:
Side length = base / cos(vertex angle)
Substituting the values, we get:
Side length = 22 cm / cos(36˚)
Calculating this value, we get approximately 27.867 cm.
Finally, plugging in this value in the perimeter formula, we have:
Perimeter = 22 cm + 22 cm + 2 * 27.867 cm
Perimeter ≈ 22 cm + 22 cm + 55.734 cm = 99.734 cm.
Therefore, the answer is approximately 99.734 cm.