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Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.

The perimeter is about____units.

Find the perimeter of the polygon with the given vertices. Round your answer to the-example-1
User SMR
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2 Answers

5 votes

Final answer:

To find the perimeter of a polygon, add the lengths of its sides obtained using the distance formula. When you have a number like 201.867, round it to 201.87 to the nearest hundredth. For adding numbers like 137.3 and 70.90, round the final sum to the tenths place, resulting in 208.2.

Step-by-step explanation:

To calculate the perimeter of a polygon, you need to know the length of all its sides and sum them up. When working with vertices, you can use the distance formula to find the length of each side. The distance formula is derived from the Pythagorean theorem and is given by:
\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the vertices. Once you've calculated the length of all sides, add them up to get the total perimeter.

In case the calculation results in a non-whole number, you might need to round the final answer. Rounding to the nearest hundredth means looking at the thousandth place. If the thousandth place is 5 or more, you round up. If it's less than 5, you round down. For example, if a calculator displays 201.867 as the perimeter, then you would round this to 201.87 since the number in the thousandths place is 7, which is greater than 5.

Similarly, when adding numbers with different decimal places, you need to be consistent with precision. If you have 137.3 in the tenths place, which is less precise, and 70.90 in the hundredths place, the final answer should be in the less precise decimal place after addition. So, 137.3 s + 70.90 s = 208.20 s would be rounded to 208.2 s to match the tenths place.

User Kavindra
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6.1k points
2 votes

Answer:

The perimeter is about 16.94 units.

Step-by-step explanation:

we know that

The perimeter of the polygon is the sum of its length sides

so


P=AB+BC+CD+DE+EF+FA

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(0,4),B(2,0)

substitute in the formula


d=\sqrt{(0-4)^(2)+(2-0)^(2)}


dAB=√(20)=4.47\ units

step 2

Find the distance BC

B(2,0),C(2,-2)

substitute in the formula


d=\sqrt{(-2-0)^(2)+(2-2)^(2)}


dBC=2\ units

step 3

Find the distance CD

C(2,-2),D(0,-2)

substitute in the formula


d=\sqrt{(-2+2)^(2)+(0-2)^(2)}


dCD=2\ units

step 4

Find the distance DE

D(0,-2),E(-2,2)

substitute in the formula


d=\sqrt{(2+2)^(2)+(-2-0)^(2)}


dDE=√(20)=4.47\ units

step 5

Find the distance EF

E(-2,2),F(-2,4)

substitute in the formula


d=\sqrt{(4-2)^(2)+(-2+2)^(2)}


dE.F=2\ units

step 6

Find the distance FA

F(-2,4),A(0,4)

substitute in the formula


d=\sqrt{(4-4)^(2)+(0+2)^(2)}


dFA=2\ units

step 7

Find the perimeter


P=4.47+2+2+4.47+2+2=16.94\ units

User Cyberboxster
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