Question

use pythagorean theorem to find perimeter
what is the perimeter of the parallelogram?
____ units
1 / 6 perimeter is the distance around a figure.
+ get another hint (1/6)

Explanation:

Step1: Identify side lengths on grid

First, count the horizontal side: it spans 8 units directly, so one pair of sides is 8 units each. For the slanted side, we use the Pythagorean theorem: the vertical rise is 6 units, horizontal run is 2 units.

Step2: Calculate slanted side length

Apply Pythagorean theorem $c = \sqrt{a^2 + b^2}$, where $a=6$, $b=2$.
$\text{Slanted side} = \sqrt{6^2 + 2^2} = \sqrt{36 + 4} = \sqrt{40} = 2\sqrt{10}$

Step3: Compute perimeter of parallelogram

Perimeter = $2\times(\text{horizontal side} + \text{slanted side})$
$= 2\times(8 + 2\sqrt{10}) = 16 + 4\sqrt{10}$
Or calculate the numerical value: $4\sqrt{10} \approx 12.65$, so $16 + 12.65 = 28.65$ (exact form is preferred).

Answer:

$16 + 4\sqrt{10}$ (or approximately 28.65) units