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A quadrilateral has vertices at (1,1), (4,2), (0,4), and (5,5). What is the perimeter of the quadrilateral?

User Vasis
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1 Answer

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21 votes

Answer:

3√10 +√26 ≈ 14.6 units

Explanation:

In order to find the perimeter of the figure, we need to determine the lengths of its sides. A plot of the points on a graph reveals that three sides are a length that is the hypotenuse of a right triangle with legs 3 units and 1 unit. Those lengths are ...

c² = a² +b²

c = √(3² +1²) = √10

The remaining longer leg is the hypotenuse of a right triangle with legs 5 units and 1 unit. Its length is ...

c = √(5² +1²) = √26

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The perimeter of the figure is the sum of its side lengths. The sum of the lengths of the three short sides and the long side is ...

3√10 +√26 ≈ 14.59 . . . units

The perimeter of the quadrilateral is about 14.6 units.

A quadrilateral has vertices at (1,1), (4,2), (0,4), and (5,5). What is the perimeter-example-1
User Aphexlog
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