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Mathematics 8 Online
OpenStudy (anonymous):

Help Plz

OpenStudy (anonymous):

OpenStudy (anonymous):

@conner143

OpenStudy (anonymous):

hey can you help me with like 15 questions plz?

OpenStudy (anonymous):

the first one is \[\sqrt{85}\] again

OpenStudy (anonymous):

\[\sqrt{162}\] is the second one

OpenStudy (anonymous):

OpenStudy (anonymous):

@Michele_Laino

OpenStudy (michele_laino):

we have to compute the base and the height of your rectangle

OpenStudy (anonymous):

I have a lot of questions...so you can just give me the answers

OpenStudy (michele_laino):

I'm sorry, I can not give you the answer directly, since I have to respect the Code of Conduct

OpenStudy (anonymous):

ok, how do we compute the height and the base of the rectangle?

OpenStudy (michele_laino):

the base of your triangle is given by the distance between points (-1,-3) and (1,3) such distance is: \[\begin{gathered} d = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} = \sqrt {{{\left( { - 1 - 1} \right)}^2} + {{\left( { - 3 - 3} \right)}^2}} = \hfill \\ = \sqrt {4 + 36} = ...? \hfill \\ \end{gathered} \]

OpenStudy (michele_laino):

whereas the height, is given by the distance between the points (1,3) and (-2,4) \[\begin{gathered} d = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} = \sqrt {{{\left( { - 2 - 1} \right)}^2} + {{\left( {4 - 3} \right)}^2}} = \hfill \\ = \sqrt {9 + 1} = ...? \hfill \\ \end{gathered} \]

OpenStudy (anonymous):

40, 10?

OpenStudy (michele_laino):

base=sqrt(40) height=sqrt(10) so: area is: \[area = \sqrt {40} \times \sqrt {10} = \sqrt {400} = ...?\]

OpenStudy (anonymous):

20

OpenStudy (michele_laino):

that's right!

OpenStudy (anonymous):

OpenStudy (michele_laino):

here the area of your polygon, is equal to area of the rectangle TSPG plus area of triangle PSE

OpenStudy (michele_laino):

now area of rectangle TSPG = 7*5=...?

OpenStudy (anonymous):

35

OpenStudy (michele_laino):

ok! and area of triangle PSE= (7*2)/2=...?

OpenStudy (anonymous):

7

OpenStudy (michele_laino):

ok! so the requested area = 35+7=...?

OpenStudy (anonymous):

42

OpenStudy (michele_laino):

that's right!

OpenStudy (anonymous):

OpenStudy (michele_laino):

here we have to break your polygon into one parallelogram, and 3 triangles, like below: |dw:1429637016712:dw|

OpenStudy (michele_laino):

area of parallelogram = 6*3=...?

OpenStudy (anonymous):

18

OpenStudy (michele_laino):

ok! area of triangle 2=(3*1)/2=...?

OpenStudy (anonymous):

1.5

OpenStudy (michele_laino):

ok! area of triangle 3= (4*3)/2=...?

OpenStudy (anonymous):

6

OpenStudy (michele_laino):

ok! area of triangle 4 = (6*3)/2=...?

OpenStudy (anonymous):

9

OpenStudy (michele_laino):

ok! so the area of your polygon is: area = 18+1.5+6+9=...?

OpenStudy (anonymous):

34.5

OpenStudy (michele_laino):

that's right!

OpenStudy (anonymous):

OpenStudy (michele_laino):

here, we to compute the base and the height of your rectangle. Now the base of your rectangle is given by the distance between the points (1,2) and (5,0), so we have: \[\begin{gathered} base = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} = \sqrt {{{\left( {5 - 1} \right)}^2} + {{\left( {0 - 2} \right)}^2}} = \hfill \\ = \sqrt {16 + 4} = ...? \hfill \\ \end{gathered} \]

OpenStudy (anonymous):

20=4.47

OpenStudy (michele_laino):

whereas the height is given by the distance between points (1,2) and (2,4), namely: \[\begin{gathered} height = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} = \sqrt {{{\left( {2 - 1} \right)}^2} + {{\left( {4 - 2} \right)}^2}} = \hfill \\ = \sqrt {1 + 4} = ...? \hfill \\ \end{gathered} \]

OpenStudy (michele_laino):

better is base = sqrt(20)

OpenStudy (anonymous):

square root of 5

OpenStudy (michele_laino):

ok! so area is: \[area = \sqrt {20} \times \sqrt 5 = \sqrt {100} = ...?\]

OpenStudy (anonymous):

10

OpenStudy (michele_laino):

ok! so we have: number of acres = 9*10=...?

OpenStudy (anonymous):

90

OpenStudy (michele_laino):

ok! so the price per acre is: 423000/90=...?

OpenStudy (anonymous):

4,700

OpenStudy (michele_laino):

that's right!

OpenStudy (anonymous):

OpenStudy (michele_laino):

here is your triangle: |dw:1429638315642:dw|

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