Question

a hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp? to find the height, first find that ∠d is approximately (square^{circ}). this means the height of the trapezoid is approximately (square) feet. so, the area of the tarp is approximately (square) square feet.

Explanation:

Step1: Find the height of the trapezoid

Draw a perpendicular from point C to the longer base (parallel to the non - parallel sides). Let's consider the right - triangle formed. The angle adjacent to the non - parallel side of length 5 ft is \(180^{\circ}- 120^{\circ}=60^{\circ}\). Using the sine function in the right - triangle, if the hypotenuse is the non - parallel side of length 5 ft and the height \(h\) is the side opposite the \(60^{\circ}\) angle. We know that \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(h = 5\sin60^{\circ}=5\times\frac{\sqrt{3}}{2}\approx5\times0.866 = 4.33\) ft.

Step2: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a = 10\) ft and \(b = 15\) ft are the lengths of the parallel sides and \(h\) is the height. Substituting the values, we get \(A=\frac{(10 + 15)\times4.33}{2}=\frac{25\times4.33}{2}=54.125\approx54\) square feet.

Answer:

The height of the trapezoid is approximately \(4.33\) feet. The area of the trapezoid is approximately \(54\) square feet. The measure of \(\angle D\) is \(60^{\circ}\).