Question

Consider parallelogram ABCD with vertices at A(−10,6), B(−5.5,26), C(9.5,18), and D(5,−2). What is the perimeter, in units, of parallelogram ABCD?

Answer 1

Given vertices of parallelogram ABCD:

A(−10,6), B(−5.5,26), C(9.5,18), and D(5,−2).

Length of AB is :

$=\sqrt{\left(-5.5-\left(-10\right)\right)^2+\left(26-6\right)^2}= 20.5$.

Length of BC is :

$=\sqrt{\left(9.5-\left(-5.5\right)\right)^2+\left(18-26\right)^2} =17.$

Note, opposite sides of a parallelogram are equal.

Therefore,

Perimeter of parallelogram ABCD = 2 × Length of AB + 2 × Length of BC.

Perimeter = 2 × 20.5 + 2 × 17

                 = 41 + 34

                 = 75 units.

Therefore, the perimeter of parallelogram ABCD is 75 units.