In trapezoid PQRS, modifying above upper P upper Q with bar parallel to modifying above upper S upper R with bar.

Trapezoid P Q R S is shown.
• At the top of the figure, horizontal segment P Q is labeled 18.
• Segment Q R angles down to the right and is labeled 24.
• Segment R S runs horizontally at the bottom of the figure.
• Segment P S angles down and to the right.
• Angle S is labeled 135 degrees.
• Angle R is labeled 35 degrees.

What is the area of PQRS in simplest radical form?
(1 point)
Responses

144 plus 72 start root 3 end root
Image with alt text: 144 plus 72 start root 3 end root

72 plus 72 start root 3 end root
Image with alt text: 72 plus 72 start root 3 end root

288 start root 3 minus 216 end root
Image with alt text: 288 start root 3 minus 216 end root

144 start root 3 minus 72 end root

1 answer

The area of trapezoid PQRS can be calculated using the formula A = (1/2)(b1 + b2)(h), where b1 and b2 are the lengths of the two parallel bases and h is the height of the trapezoid.

In this case, b1 = 18, b2 = 24, and h can be calculated using trigonometry. Using angle R, we can determine that h = PS = RS * sin(R) = 24 * sin(35 degrees).

Now we can plug these values into the formula:

A = (1/2)(18 + 24)(24 * sin(35 degrees))
A = (1/2)(42)(24 * 0.574)
A = (21)(13.776)
A = 288

Therefore, the area of trapezoid PQRS is 288.