Find the perimeter of a quadrilateral with vertices at C (−2, 4), D (−3, 1), E (1, 0), and F (−1, 2). Round your answer to the nearest hundredth when necessary. 10 units
10.77 units
11.52 units
12.35 units

Perimeter of quadrilateral =  12.35 units

Explanation:

To find - Find the perimeter of a quadrilateral with vertices at C (−2, 4), D (−3, 1), E (1, 0), and F (−1, 2).

Proof -

The figure becomes :

We have the points -

C (−2, 4),

D (−3, 1),

E (1, 0),

F (−1, 2)

Now,

We know that -

The perimeter = Distance of (CD + DE + EF + FC)

Now,

Distance of CD = √(-3 + 2)² + (1 - 4)²

                         = √(-1)² + (-3)²

                         = √1 + 9

                         = √10 = 3.16

⇒Distance of CD = 3.16

Now,

Distance of DE = √(1 + 3)² + (0 - 1)²

                         = √(4)² + (-1)²

                         = √16 + 1

                         = √17 = 4.12

⇒Distance of DE = 4.12

Now,

Distance of EF = √(-1 - 1)² + (2 - 0)²

                         = √(-2)² + (2)²

                         = √4 + 4

                         = √8 = 2.83

⇒Distance of EF = 2.83

Now,

Distance of FC = √(-2 + 1)² + (4 - 2)²

                         = √(-1)² + (2)²

                         = √1 + 4

                         = √5 = 2.24

⇒Distance of FC = 2.24

So,

Perimeter of quadrilateral = 3.16 + 4.12 + 2.83 + 2.24

                                           = 12.35 units

⇒Perimeter of quadrilateral =  12.35 units