Answer:
4√5 + 4√10
Explanation:
The perimeter is the sum of all the sides.
Using the coordinates given to us, we can find the sides of the quadrilateral.
d(ab) = √[(x2 - x1)² + (y2 - y1)²]
Given that, we apply that to each and every of the side, and thus we have
d(le) = √[(3 --3)² + (3 - 1)²]
d(le) = √[(6²) + (2)²]
d(le) = √(36 + 4)
d(le) = √40
d(ea) = √[(5 - 3)² + (7 - 3)²]
d(ea) = √[(2)² + (4²)]
d(ea) = √(4 + 16)
d(ea) = √20
d(ap) = √[(-1 - 5)² + (5 - 7)²]
d(ap) = √[-6)² + (-2)²]
d(ap) = √(36 + 4)
d(ap) = √40
d(pl) = √[(-1 --3)² + (5 - 1)²]
d(pl) = √[(-2)² + (4)²]
d(pl) = √(4 + 16)
d(pl) = √20
Perimeter of the quadrilateral is then
d(le) + d(ea) + d(ap) + d(pl)
√40 + √20 + √40 + √20
4√5 + 4√10