Quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent
Now, let's find the slopes of the sides using the Slope Formula.
Side
Slope Formula
Simplified
Slope of QR: ( 0,3), ( 5,5)
5- 3/5- 0
2/5
Slope of RS: ( 5,5), (3,0)
- 5/3- 5
5/2
Slope of ST: (3,0), (0, 0)
-/-3
0
Slope of TQ: (0, 0), ( 0,3)
3-/0-
Undefined
We have found that the quadrilateral has no parallel sides. Therefore, we need to continue by finding the lengths of its sides. For that we will use the Distance Formula.
Side
Distance Formula
Simplified
Length of QR: ( 0,3), ( 5,5)
sqrt(( 5- 0)^2+( 5- 3)^2)
sqrt(29)
Length of RS: ( 5,5), ( 3,0)
sqrt(( 3- 5)^2+( 0- 5)^2)
sqrt(29)
Length of ST: ( 3,0), ( 0, 0)
sqrt(( 0- 3)^2+( 0- 0)^2)
3
Length of TQ: ( 0, 0), ( 0,3)
sqrt(( 0- 0)^2+( 3- 0)^2)
3
Our parallelogram has two pairs of consecutive sides congruent and no opposite sides congruent. Therefore, the most precise name for this quadrilateral is a kite.
Area
To find the area, we can use the formula for the area of a kite.
A=1/2d_1d_2
In this case we need to find the length of the diagonals, d_1=QS and d_2=RT.
Side
Distance Formula
Simplified
Length of QS: ( 0,3), ( 3,0)
sqrt(( 3- 0)^2+( 0- 3)^2)
sqrt(18)
Length of RT: ( 5,5), ( 0, 0)
sqrt(( 0- 5)^2+( 0- 5)^2)
sqrt(50)
Let's substitute these values into the formula to find A.
A= 1/2(sqrt(18))(sqrt(50)) ⇔ A=15
The area of our kite is 15 units squared.
