Question

(06.04 MC)

Find the perimeter of the image below:

Answer 1

The coordinates are P(-2,11), Q(-4,5), R(2,0), S(1,7), T(8,7)

The distance formula gives the length of each side


$PQ = \sqrt{(-2 - -4)^2 + (11-5)^2} = \sqrt{40}=2\sqrt{10}$
$QR=\sqrt{(-4 - 2)^2+(5-0)^2}=\sqrt{61}$
$RS=\sqrt{(2-1)^2+(0-7^2)}=\sqrt{50}=5 \sqrt{2}$
$ST = 7$
$PT=\sqrt{(-2 - 8)^2 + (11 -7)^2} = \sqrt{116} = 2 \sqrt{29}$

Perimeter = $2\sqrt{10} +\sqrt{61}+ 5 \sqrt{2} + 7 + 2 \sqrt{29}$

That's exact and won't simplify particularly nicely so let's stop here.  Run it through the calculator if you like.

Answer 2

Hello!

As you can see, all of the edges of this shape are slanted except for ST, therefore we need to find the distance between each slanted point. To do so we connect two points with two lines, making a right triangle, where the slant is the hypotenuse. We will use the Pythagorean Theorem (a²+b²=c²)  to solve for each side.

   PT
100+16=116
 √116
PT≈10.77

    SR
1+49=50
   √50
 SR≈7.07

     RQ
36+25=61
√61
RQ≈7.81

      QP
36+4=40
√40
QP≈6.32

ST=7

Now we add up all of our values.

10.77+7.07+7.81+6.32+7=38.97

Therefore, the perimeter of this figure is about 38.97 units.

I hope this helps!