Question

What is the perimeter of the trapezoid with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8)? Round to the nearest hundredth, if necessary.

Answer 1

Check the picture below.

so... you can pretty much see how long RS and QT are, you can just count the units off the grid.

now, let's find QR's length

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &Q&(~ 8 &,& 8~) % (c,d) &R&(~ 14 &,& 16~) \end{array}~~ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ QR=\sqrt{(14-8)^2+(16-8)^2}\implies QR=\sqrt{6^2+8^2} \\\\\\ QR=\sqrt{36+64}\implies QR=\sqrt{100}\implies QR=10$

and let's also find the length for ST

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &S&(~ 20 &,& 16~) % (c,d) &T&(~ 22 &,& 8~) \end{array}~ d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ ST=\sqrt{(22-20)^2+(8-16)^2}\implies ST=\sqrt{2^2+(-8)^2} \\\\\\ ST=\sqrt{4+64}\implies ST=\sqrt{68}\implies ST=\sqrt{4\cdot 17} \\\\\\ ST=\sqrt{2^2\cdot 17}\implies ST=2\sqrt{17}$

so, add the lengths of all sides, and that's the perimeter of the trapezoid.

Answer 2

Answer:

The Perimeter is 38.25 units.

Step-by-step explanation:

The vertices of trapezoid are Q(8, 8), R(14, 16), S(20, 16), and T(22, 8). we have to find the perimeter of trapezoid.

Perimeter is sum of all sides of trapezoid i.e

Perimeter=QR+RS+ST+TQ

By distance formula,

$QR=\sqrt{(16-8)^2+(14-8)^2}=\sqrt{64+36}=\sqrt{100}=10 units\\\\RS=\sqrt{(20-14)^2+(16-16)^2}=\sqrt{6^2}=6units\\\\ST=\sqrt{(22-20)^2+(8-16)^2}=\sqrt{4+64}=\sqrt{68}=8.25units\\\\TQ=\sqrt{(8-22)^2+(8-8)^2}=\sqrt{14^2}=14units$

Perimeter=QR+RS+ST+TQ

                =10+6+8.25+14=38.25 units.