Question
In trapezoid PQRS, . • 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 Image with alt text: 144 plus 72 start root 3 end root Image with alt text: 72 plus 72 start root 3 end root Image with alt text: 288 start root 3 minus 216 end root
Answers
GPT 3.5
To find the area of trapezoid PQRS, we need to first find the length of segment PS.
Using trigonometry, we can find the length of PS:
tan(135 degrees) = PS / 18
PS = 18 * tan(135 degrees)
PS = 18 * (-1)
PS = -18
Next, we can find the area of the trapezoid:
Area = 1/2 * (18 + 24) * (18 - (-18))
Area = 1/2 * 42 * 36
Area = 21 * 36
Area = 756
Therefore, the area of trapezoid PQRS is 756.
Using trigonometry, we can find the length of PS:
tan(135 degrees) = PS / 18
PS = 18 * tan(135 degrees)
PS = 18 * (-1)
PS = -18
Next, we can find the area of the trapezoid:
Area = 1/2 * (18 + 24) * (18 - (-18))
Area = 1/2 * 42 * 36
Area = 21 * 36
Area = 756
Therefore, the area of trapezoid PQRS is 756.