+128474
5. We first need to find the height of the triangle.....this will also equal the height of the trapezoid on the left
Since the height of the triangle is opposite a 30 degree angle in a 30 - 60 - 90 triangle, its measure is 1/2 of the hypotenuse = 12
And the base is opposite the 60 degree angle....so its length is (√3/2) * hypotenuse = (√3/2)*24 = 12√3
So.....the area of the triangle = 1/2 base * height = (1/2) (12√3)(12) = 72√3
The figure on the right is a trapezoid....its area = (1/2) Height ( Top Base + Bottom Base) =
(1/2)(12) (18 + 6) = 6 * 24 = 144
So.....the correct answer is 144 + 72√3
6. Area of kite = (1/2) product of the diagonals =
(1/2) (5.3 * 6) = 15.9 ft^2
