select the correct answer from each drop - down menu. a hotel builds an isosceles trapezoidal pool for…

select the correct answer from each drop - down menu. 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 °. this means the height of the trapezoid is approximately feet. so, the area of the tarp is approximately square feet.

select the correct answer from each drop - down menu. 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 °. this means the height of the trapezoid is approximately feet. so, the area of the tarp is approximately square feet.

Answer

Explanation:

Step1: Find angle D

In an isosceles trapezoid, base - angles are equal. Since $\angle C = 120^{\circ}$, and $\angle C+\angle D=180^{\circ}$ (adjacent - angles along a non - parallel side of a trapezoid are supplementary), then $\angle D = 60^{\circ}$.

Step2: Find the height of the trapezoid

Let's consider the right - triangle formed by dropping a perpendicular from point C to AD. If the non - parallel side of the trapezoid is $l = 5$ ft and the angle between the non - parallel side and the base is $\angle D=60^{\circ}$, and the height $h$ of the trapezoid is related to the non - parallel side by $\sin\angle D=\frac{h}{l}$. So $h = l\sin\angle D=5\sin60^{\circ}=5\times\frac{\sqrt{3}}{2}\approx5\times0.866 = 4.33$ ft.

Step3: Calculate the area of the trapezoid

The area formula of a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$, where $b_1 = 10$ ft, $b_2 = 15$ ft and $h\approx4.33$ ft. Then $A=\frac{(10 + 15)\times4.33}{2}=\frac{25\times4.33}{2}=54.125$ square feet.

Answer:

$\angle D$ is $60^{\circ}$, the height of the trapezoid is approximately $4.33$ feet, and the area of the tarp is approximately $54.125$ square feet.