In trapezoid PQRS, PQ ∥ SR.
What is the area of PQRS in simplest radical form?
Image: www(dot)connexus(dot)com/content/media/941080-7222013-111302-AM-598825301(dot)gif
a. 50 + 50√3
b. 110 + 50√3
c. 110√3 - 50
d. 210√3 = 150
We can find the area of trapezoid PQRS using the formula:
A = 1/2 (base1 + base2) x height
Since PQ and SR are parallel, we can see that base1 = PQ and base2 = SR. To find the height, we can draw a perpendicular line segment from P to SR, and call the point where it intersects SR "T". Then, we can see that triangle PQT is a 30-60-90 triangle (because PQ = QR), and the height of the trapezoid from P to SR is equal to QT.
Using the properties of 30-60-90 triangles, we can see that QT = PQ/2 times the square root of 3. Therefore:
A = 1/2 (PQ + SR) x QT
A = 1/2 (PQ + SR) x (PQ/2 times the square root of 3)
A = 1/4 (PQ^2) times the square root of 3 + (PQ x SR) / 2
To find the area of PQRS, we need to find PQ and SR. We can see from the diagram that PQ = 10 and SR = 20.
Plugging these values into our formula:
A = 1/4 (10^2) times the square root of 3 + (10 x 20) / 2
A = 25 times the square root of 3 + 100
Simplifying:
A = 100 + 25 times the square root of 3
Therefore, the answer is (a) 50 + 50 times the square root of 3.
To find the area of trapezoid PQRS, we can use the formula:
Area = 1/2 * (sum of the parallel sides) * (distance between the parallel sides)
In this case, the parallel sides are PQ and SR, and we're given that PQ is parallel to SR.
Looking at the image, we can see that the length of PQ is 20 units and the length of SR is 50 units.
Next, we need to find the distance between the parallel sides. From the image, we can see that the perpendicular distance between PQ and SR is 10 units.
Using the formula, we can calculate the area as follows:
Area = 1/2 * (20 + 50) * 10
= 1/2 * 70 * 10
= 350
Therefore, the area of trapezoid PQRS is 350 square units. However, none of the answer choices match this result. Please double-check the provided answer choices or provide more information for further assistance.