Quadrilateral PQRS is drawn with the following information labeled:
· Side PQ is 8 feet.
· Side QR is 13 feet.
· Side RS is 8 feet.
· Side SP is 13 feet.
· Angle Q is 120 degrees.
Quadrilateral TUVW is drawn with the following information labeled:
· Side TU is 5.2 feet.
· Side UV is 2.4 feet.
· Side VW is 5.2 feet.
· Side WT is 2.4 feet.
· Angle T is 120 degrees.
I'm clueless
What is your question?
I sketched the first one,
if you join PR, you can see that you have 2 congruent triangles, so angle S = 120°
by the sine law you can find the other angles and PR
the other question is the same thing.
To analyze these two quadrilaterals, we can start by determining their shapes.
For Quadrilateral PQRS, given the given side lengths and angle measures, we can determine that it is an isosceles trapezoid (a quadrilateral with one pair of parallel sides). The parallel sides are PQ and RS, while the non-parallel sides are QR and SP.
For Quadrilateral TUVW, with the given side lengths and angle measures, we can determine that it is a parallelogram (a quadrilateral with opposite sides parallel and equal in length).
Now, let's analyze the properties of each quadrilateral more closely.
- Quadrilateral PQRS:
1. Calculate the perimeter of PQRS: Add up the lengths of all four sides:
Perimeter = PQ + QR + RS + SP = 8 + 13 + 8 + 13 = 42 feet.
2. Determine the area of PQRS:
To find the area of an isosceles trapezoid, we can use the formula:
Area = ((sum of the lengths of the parallel sides)/2) * (height)
Since PQ and RS are parallel sides, we can use the formula:
Area = ((PQ + RS)/2) * (QR or SP)
Area = ((8 + 8)/2) * 13 = 8 * 13 = 104 square feet.
- Quadrilateral TUVW:
1. Calculate the perimeter of TUVW: Add up the lengths of all four sides:
Perimeter = TU + UV + VW + WT = 5.2 + 2.4 + 5.2 + 2.4 = 15.2 feet.
2. Determine the area of TUVW:
To find the area of a parallelogram, we can use the formula:
Area = (base) * (height).
Since opposite sides in a parallelogram are parallel and equal in length, we can choose any side as the base and the distance between the parallel sides as the height.
Area = TU * (VW or UV) = 5.2 * 2.4 = 12.48 square feet.
So, to recap:
- The perimeter of Quadrilateral PQRS is 42 feet.
- The area of Quadrilateral PQRS is 104 square feet.
- The perimeter of Quadrilateral TUVW is 15.2 feet.
- The area of Quadrilateral TUVW is 12.48 square feet.