Question

Quadrilateral MNOP has vertices M(-3,4), N(-1,4), O(4,-5), P(2,-5). What is the approximate perimeter of the quadrilateral?

Answer 1

The perimeter of a shape is the sum of its side lengths

The perimeter of the quadrilateral is approximately 25 units

How to determine the perimeter

The vertices of the quadrilateral MNOP are given as:

M = (-3,4)

N = (-1,4)

O = (4,-5)

P = (2,-5)

Start by calculating the lengths of the side lengths using the following distance formula

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

So, we have:

$MN = \sqrt{(-1 +3)^2 + (4 -4)^2} = 2$

$NO = \sqrt{(4+1)^2 + (-5 -4)^2} \approx 10.3$

$OP = \sqrt{(2-4)^2 + (-5 +5)^2} =2$

$PM = \sqrt{(-3-2)^2 + (4+5)^2} \approx 10.3$

The perimeter is then calculated as:

$P = 2 + 10.3 + 2 +10.3$

Add

$P = 24.6$

Approximate

$P = 25$

Hence, the perimeter of the quadrilateral is approximately 25 units

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