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stira [4]
3 years ago
11

What is the area of this figure? Enter your answer in the box.

Mathematics
2 answers:
ElenaW [278]3 years ago
7 0
Area
=3*2/2+6*1/2+3*6/2+(6+7)*6/2
=54

aliina [53]3 years ago
4 0

Answer:

Area of Figure = 54 unit^2

Step-by-step explanation:

Given Graph of a polygon with 7 side.

To find: Area of figure

First we write coordinates of all vertices from left bottom going in clock wise direction.

Say, Vertex A ( -3, -3 ) , Vertex B ( 4, -3 ) , Vertex C ( 4, 3 ) , Vertex D ( 3, 4 ) , Vertex E ( -2, 3 ) , Vertex F ( -4, 5 ) , Vertex  G ( -5, 3 )

Now we divide the given figure in a trapezium ABCG and 2 triangle ΔCDE , ΔEFG

Area of Trapezium = \frac{1}{2}\times height\times (sum of parallel sides)

From Figure, Height , BC = 6 unit and Parallel side, AB = 7 unit , CG = 9 units

⇒ Area of Trapezium = \frac{1}{2}\times BC\times(AB+CG)

                                    = \frac{1}{2}\times 6\times(7+9)

                                    = 3\times(16)

                                    = 48 unit^2

Now for area of triangle we use Area of triangle using coordinates. Given by,

Area\: of\: Triangle\: =\:\frac{1}{2}\times\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|

⇒ Area of ΔCDE = \frac{1}{2}\times\left|4(4-3)+3(3-3)+(-2)(3-4)\right|

                            = \frac{1}{2}\times\left|4\times1+3\times0+(-2)\times(-1)\right|

                            = \frac{1}{2}\times\left|4+0+2\right|

                            = \frac{1}{2}\times6

                            = 3 unit^2

Similarly,

⇒ Area of ΔEFG = \frac{1}{2}\times\left|(-5)(3-5)+(-2)(5-3)+(-4)(3-3)\right|

                            = \frac{1}{2}\times\left|(-5)\times(-2)+(-2)\times2+(-4)\times0\right|

                            = \frac{1}{2}\times\left|10-4+0\right|

                            = \frac{1}{2}\times6

                            = 3 unit^2

∴ Area of Figure = area of trapezium ABCG + area of ΔCDE + area of ΔEFG

                           = 48 + 3 + 3

                           = 54 unit^2

Therefore, Area of Figure = 54 unit^2

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Four times the amount of money in my bank account plus $200 is still two
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Answer:

$700

Step-by-step explanation:

So, I like to extract the information we know and form it into an equation.

So we know that after multiplying what you have in the bank by 4, then add 200 dollars you get two thousand dollars less than a fourth of what's in your dad's bank account.

Your dad has $20,000 in the bank.

Before we write the equation let's find what two thousand less than a fourth of 20,000 is.

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we can isolate the variable by subtracting 200 from both sides

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