Answer:
The perimeter of the trapezoid is [tex]38.25\ units[/tex]
Step-by-step explanation:
we know that
The perimeter of the trapezoid is the sum of its four side lengths
so
In this problem
[tex]P=QR+RS+ST+QT[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]Q(8, 8), R(14, 16), S(20, 16),T(22, 8)[/tex]
step 1
Find the distance QR
[tex]Q(8, 8), R(14, 16)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(16-8)^{2}+(14-8)^{2}}[/tex]
[tex]d=\sqrt{(8)^{2}+(6)^{2}}[/tex]
[tex]d=\sqrt{100}[/tex]
[tex]QR=10\ units[/tex]
step 2
Find the distance RS
[tex]R(14, 16), S(20, 16)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(16-16)^{2}+(20-14)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]RS=6\ units[/tex]
step 3
Find the distance ST
[tex]S(20, 16),T(22, 8)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(8-16)^{2}+(22-20)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{68}[/tex]
[tex]ST=8.25\ units[/tex]
step 4
Find the distance QT
[tex]Q(8, 8),T(22, 8)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(8-8)^{2}+(22-8)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(14)^{2}}[/tex]
[tex]d=\sqrt{196}[/tex]
[tex]QT=14\ units[/tex]
step 5
Find the perimeter
[tex]P=10+6+8.25+14=38.25\ units[/tex]
