Question

Parallelogram ABCD has vertices A(1,1) , B(17,1) , C(22,13) , and D(6,13) what is the perimeter in units of parallelogram ABCD

Answer 1

Answer:

The perimeter is equal to $58\ units$

Step-by-step explanation:

we know that

Opposite sides of a parallelogram are parallel and congruent

Plot the figure

we have

$A(1,1) , B(17,1) , C(22,13) , D(6,13)$

so

AB=DC

AD=BC

see the attached figure

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance AB

$A(1,1),B(17,1)$

substitute the values

$dAB=\sqrt{(1-1)^{2}+(17-1)^{2}}$

$dAB=\sqrt{(0)^{2}+(16)^{2}}$

$dAB=16\ units$

step 2

Find the distance AD

$A(1,1),D(6,13)$

substitute the values

$dAD=\sqrt{(13-1)^{2}+(6-1)^{2}}$

$dAD=\sqrt{(12)^{2}+(5)^{2}}$

$dAD=13\ units$

step 3

Find the perimeter of the parallelogram

P=AB+DC+AD+BC

substitute the values

$P=2(16)+2(13)=58\ units$

Answer 2

The perimeter of the parallelogram, in units is: 58 units.

What is the Perimeter of a Parallelogram?

Perimeter = sum of all the sides of the parallelogram.

What is the Distance Formula?

Distant formula = $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Given:

• A(1,1)
• B(17,1)
• C(22,13)
• D(6,13)

Perimeter = AB + BC + CD + DA

Use the distance formula to find length of each segment:

AB = √[(17−1)² + (1−1)]²

AB = √256 = 16 units

Following the same step, we would have:

BC = 13 units

CD = 16 units

DA = 13 units

Therefore:

Perimeter of the parallelogram = 16 + 13 + 16 + 13 = 58 units.

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