Question

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 \\(\angle d\\) is 60\\(^{\circ}\\). this means the height of the trapezoid is approximately 4.3 feet. so, the area of the tarp is approximately choose an answer square feet.

options for the last drop-down:
53.8
38.5
47.3

Explanation:

⚡ Using what you learned: Area of Trapezoids and Other Polygons

Step 1: Find the measure of \(\angle D\)

In an isosceles trapezoid, consecutive angles between the parallel bases are supplementary:

$$ \angle C + \angle D = 180^\circ $$

$$ 120^\circ + \angle D = 180^\circ $$

$$ \angle D = 60^\circ $$

Step 2: Find the height of the trapezoid

Draw a perpendicular height \(h\) from vertex \(C\) to the base \(AD\). This forms a right triangle with the slant side \(CD = 5\text{ ft}\) as the hypotenuse:

$$ h = 5 \cdot \sin(60^\circ) $$

$$ h = 5 \cdot \frac{\sqrt{3}}{2} \approx 4.33\text{ ft} $$

The height is approximately \(4.3\text{ ft}\).

Step 3: Calculate the area of the trapezoid

Using the area formula for a trapezoid:

$$ \text{Area} = \frac{1}{2} \cdot (b_1 + b_2) \cdot h $$

$$ \text{Area} = \frac{1}{2} \cdot (10 + 15) \cdot 4.33 $$

$$ \text{Area} = \frac{1}{2} \cdot 25 \cdot 4.33 \approx 54.1\text{ sq ft} $$

Using the rounded height of \(4.3\text{ ft}\):

$$ \text{Area} \approx \frac{1}{2} \cdot 25 \cdot 4.3 = 53.75\text{ sq ft} $$

This rounds to \(53.8\text{ sq ft}\).

Answer:

• To find the height, first find that \(\angle D\) is 60\(^\circ\).
• This means the height of the trapezoid is approximately 4.3 feet.
• So, the area of the tarp is approximately 53.8 square feet.