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

CPhill
Apr 21, 2017