Question

PLS HELPP!! Will Venmo for answer!!! The figure below shows trapezoid ABCD on a coordinate plane. Which of the following expressions represents the perimeter of this figure in units?

Answer 1

Option (4)

Explanation:

Coordinates of the vertices of the given trapezoid,

A(-9, 4), B(-4, -3), C(2, -4), D(9, 1) and E(-3, 3)

Perimeter of ABCD = length of AB + length of BC + length of CD + length of DA

Length of AB =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

=
`√((-9+4)^2+(4+3)^2)`

=
`√(25+49)`

=
`√(74)`

Length of BC =
`√((-4-2)^2+(-3+4)^2)`

=
`√(36+1)`

=
`√(37)`

Length of CD =
`√((2-9)^2+(-4-1)^2)`

=
`√(49+25)`

=
`√(74)`

Length of DA =
`√((-9-9)^2+(4-1)^2)`

=
`√(324+9)`

=
`√(333)`

Perimeter of ABCD =
`√(74)+√(37)+√(74)+√(333)`

=
`√(74)+√(37)+√(74)+3√(37)`

=
`4√(37)+2√(74)`

Therefore, Option (4) will be the answer.