Answer:
Since the triangle is isosceles, the base angles are equal, and each measures (180 - 36) / 2 = 72 degrees. We can draw an altitude from the vertex angle to the base, which bisects the base and divides it into two equal segments. This altitude also bisects the vertex angle into two equal angles of 18 degrees each. We can use trigonometry to find the length of the altitude.Let h be the length of the altitude. Then, we have:tan(18) = h / (2 / 2)tan(18) = hUsing a calculator, we get:h ≈ 0.94 feetNow, we can use the formula for the area of a triangle:A = (1/2)bhwhere b is the length of the base and h is the length of the altitude. Substituting the values we have:A = (1/2)(2)(0.94)A ≈ 0.94 square feetTherefore, the area of the isosceles triangle with legs of 2 feet each and a vertex angle of 36 degrees is approximately 0.94 square feet.
Explanation: