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antiseptic1488 [7]
2 years ago
6

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

Mathematics
1 answer:
Korolek [52]2 years ago
6 0

Perimeter of the given polygon is 16.94 units.

To measure the distance between two points (x_1,y_1) and (x_2,y_2) is given by the ex[pression,

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

By using this expression,

Distance between A(0, 4) and B(2, 0) = \sqrt{(0-2)^2+(4-0)^2}

                                                              = \sqrt{20} units

Distance between B(2, 0) and C(2, -2) = \sqrt{(2-2)^2+(0+2)^2}

                                                               = 2 units

Distance between C(2, -2) and D(0, -2) = \sqrt{(0-2)^2+(-2+2)^2}

                                                                 = 2 units

Distance between D(0 -2) and E(-2, 2) = \sqrt{(0+2)^2+(-2-2)^2}

                                                                = \sqrt{20} units

Distance between E(-2, 2) and F(-2, 4) = \sqrt{(-2+2)^2+(2-4)^2}

                                                               = 2 units

Distance between F(-2, 4) and A(0, 4) = \sqrt{(-2-0)^2+(4-4)^2}

                                                               = 2 units

Perimeter of ABCDEF = AB + BC + CD + DE + EF + FA

                                     = \sqrt{20}+2+2+\sqrt{20}+2+2

                                     = 8+2\sqrt{20}

                                     = 16.94 units

      Therefore, perimeter of the given polygon in the graph attached is 16.94 units.

Learn more,

brainly.com/question/17248544

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\large\bf{\underline{Answer:}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{ = 3000 \:ft^2}

__________________________________________

\large\bf{\underline{Given:}}

  • A 3 dimensional figure with 5 sides
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  • And 2 triangles with base =30 ft and height = 20 ft

\large\bf{\underline{To\: find:}}

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\large\bf{\underline{Therefore:}}

\bf{area \:of\: figure}

‎ㅤ{\bf = area \:of \:3\: rectangles + 2 \: triangles}

\large\bf{\underline{Formulas:}}

\boxed{\bf\pink{area\:of\: triangle= \frac{1}{2}\times base\times height}}

\boxed{\bf\pink{area\:of\: rectangle=length\times breadth}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{= 3\times (28 \times 25 )+ 2(\frac{1}{2} \times 30 \times 20)}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{= 3 \times 800 + 2 \times 300}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{=2400+ 600}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{= 3000}

__________________________________________

\large\bf{\underline{Hence,}}

❒ Area of given figure

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\huge\mathfrak{= 3000\: ft^2}

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