What is the perimeter of the trapezoid with vertices eQ(8,8), R(14,16), S(20,16), and T(22,8)?

Perimeter of a trapezoid is the sum of lengths of all of its sides. We are given the vertices of the trapezoid, using the distance formula we can calculate the length of all the sides of the trapezium and hence calculate the perimeter.

Distance formula is:

[tex]\sqrt{(x_{2} -x_{1} )^{2}+ (y_{2} -y_{1} )^{2} }[/tex]

here x1, y1 are the coordinates of 1st point and x2, y2 are the coordinates of 2nd point respectively. Using this formula for given points, we get:

[tex]QR=\sqrt{(14-8)^{2}+ (16-8)^{2} }=10\\\\ RS=\sqrt{(20-14)^{2}+ (16-16)^{2} }=6\\\\ST=\sqrt{(22-20)^{2}+ (8-16)^{2} }=8.25\\\\TQ=\sqrt{(8-22)^{2}+ (8-8)^{2} }=14\\[/tex]

Perimeter of Trapezoid = Sum of all 4 sides

= 10 + 6 + 8.25 + 14

= 38.25

Thus, the perimeter of trapezoid with given vertices is 38.25 units.

imlittlestar imlittlestar · Answer 2 · 2019-04-26T02:29:38+02:00

Answer:

Perimeter = 38.25 units

Step-by-step explanation:

Points to remember

Distance formula

Let (x₁, y₁) and (x₂, y₂) be the point

Length = √[(x₂ - y₂)² + (y₂ - y₁)²]

It is given that, a trapezoid with vertices Q(8,8), R(14,16), S(20,16), and T(22,8)

To find the length of sides

Using distance formula we get,

QR = 10, RS = 6, ST = 8.25 and QT = 14

To find the perimeter

Perimeter = QR + RS + ST = QT

= 10 + 6 + 8.25 + 14 = 38.25