find the area of the shaded polygons

Find The Area Of The Shaded Polygons

Answers

Answer 1

Answer:

  4 square units

Step-by-step explanation:

The vertices of the figure are on grid points, so it is appropriate to use Pick's theorem to find the area.

__

formula

Pick's theorem tells you the area is ...

  A = i +b/2 -1

where i is the number of grid points interior to the figure (0), and b is the number of grid points on the boundary (10).

application

Using the counted values in the formula, we find the area to be ...

  A = 0 +10/2 -1 = 4

The area of the polygon is 4 square units.

_____

Additional comment

There are several other ways to find the area. Here are a couple:

decompose the figure

A horizontal line 1 unit up from the bottom will divide the figure into a trapezoid and a triangle. The trapezoid has bases 4 and 1, and height 1, so its area is ...

  A = 1/2(b1 +b2)h = 1/2(4 +1)(1) = 5/2

The triangle has base 1 and height 3, so its area is ...

  A = 1/2bh = 1/2(1)(3) = 3/2

Then the total area is 5/2 +3/2 = 8/2 = 4 square units.

subtract empty space

The figure occupies a 4×4 square with triangles removed from the left side and the top. Each of those triangles has a base of 4 and a height of 3. The remaining (shaded) area is ...

  A = s² -1/2bh -1/2bh

  A = 4² -1/2(4)(3) -1/2(4)(3) = 16 -12 = 4 square units


Related Questions

The height in feet of 25 trees is shown below (lowest to highest). 25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54

outlier if any

Answers

There are no outliers in the dataset of the heights in feet of 25 trees

How to determine the presence of outliers?

The sorted dataset is given as:

25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54

Outliers are relatively far from other elements of the dataset.

The highest and the least elements are 54 and 25, respectively.

Other elements of the dataset are relatively close to these two elements

Hence, there are no outliers in the dataset of the heights in feet of 25 trees

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Give the standard form 80,000+200+2

Answers

Answer:

80,202 = 8.0202 × 10⁴

Find the distance between the points (5,0) and (-5,3)

Answers

Answer:

10.4

Step-by-step explanation:

√(5--5)²+(0-3)²

√100+9

√109=10.4

Thandi has decided to make grocery combo’s for her shop. The wholesaler where she buys from, sells sugar in packets of 20 in a carton, flour in packets of 12 a carton, and there are 15 bags of rice in a carton. How many of each item should she buy so there are an equal number of packets of sugar, packets of flour and bags of rice in each combo?

Answers

Answer:

3 cartons of sugar 5 cartons of flour and 4 cartons of rice

Step-by-step explanation:

First find the least common factor being 60 then divide by the number of packets each carton comes with to find how many cartons you need of each

Silas is researching the cost of a specific souvenir he wants to buy on his international trip. Use the table to answer the question.​

Answers

Answer:

Egypt.

Step-by-step explanation:

We need to set up our conversion factors for each currency.

British Pounds and Egyptian Pounds:

0.83 £ (Europe) = 1 U.S. Dollar

18 E£ (Egypt) = 1 U.S. Dollar

Cost of a Souvenir in Europe:

The cost of souvenir in Europe is 13£. Using our conversion rate, we get

[tex]13\pounds \cdot \frac{\$1}{0.83 \pounds}=\$15.66[/tex]

Cost of a Souvenir in Egypt:

The cost of a souvenir in Egypt is 342 E£. So we have

[tex]342 \text{ E}\pounds\cdot \frac{\$1}{18 \text{ E}\pounds}=\$19[/tex]

Based on our calculations, it is cheaper to buy a souvenir in Europe than in Egypt.

hope you do well in math and thx for the help

Answers

[tex]|\Omega|=12^2=144\\|A|=4^2+3^2+5^2=16+9+25=50\\\\P(A)=\dfrac{50}{144}=\dfrac{25}{72}\approx35\%[/tex]

The ratio of black bags to blue bags is 5to 3 if there are a total of 10 black bags ,then how many blue bags are there

Answers

Answer:

6

Step-by-step explanation:

We can think of the 10 black bags as 2 sets of 5-black bags (10 divided into groups of 5; 10 / 5 ; is 2 groups/sets). So, we would also have two sets of 3 (3 x 2 = 6), or 6 bags.

5 : 3 = 10 : 6

(multiply both numbers by 2)

Find the number of students that play

A basketball and football but not volleyball
B basketball only
C none
#15 play
basketball and volleybal

Answers

Answer:

#16 play basketball and football

⚠️WILL GIVE BRAINLIEST⚠️Which equation represents circle N?




A.

(x + 7)2 + (y − 6)2 = 25

B.

(x − 7)2 + (y + 6)2 = 25

C.

(x + 7)2 + (y − 6)2 = 50

D.

(x − 7)2 + (y + 6)2 = 50

Answers

Answer:

your answer is option C

Step-by-step explanation:

hope you can understand

Answer:

The answer is indeed C, (x + 7)2 + (y − 6)2 = 50

Step-by-step explanation:

Got it right on edmentum/plato, the other guy is correct. Give him brainliest!

6 liters of a gas has a pressure of 4 atmospheres. The gas's original pressure was 6 atmospheres.

What was the original volume in liters?

Enter your answer as a decimal to the 10th place, like this: 4.2 l

Answers

The original volume of the gas was 9.0 liters.

What is proportion?

Proportion is a mathematical expression of quantities in their rate form.

Analysis:

If 6 liters of the gas has a pressure of 4 atmosphere.

Then 1 atmosphere of the gas is 6/4 liters

Therefore 6 atmospheres = 6/4 x 6 = 9.0 liters

In conclusion, the Original volume of the gas was 9.0 liters

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Write an equation for a line perpendicular to y = − 4 x + 5 and passing through the point (-12,-4)

Answers

Answer:

[tex]y=\frac{1}{4} x-1.[/tex]

Step-by-step explanation:

1) if the lines are perpendicular, then the second slop is 0.25;

2) the equation of the 2d line is y=0.25x+i, where i - unknown intercept;

3) it is possible to calculate the unknown intercept, if to substitute the given coordinates into the equation y=0.25x+i:

-4=-12*0.25+i; ⇔ i=-1.

4) finally, the required equation is:

[tex]y=\frac{1}{4} x-1.[/tex]

I need to find values of product and quotient functions

Answers

The answers are 8 and 2

What is a function?

A function is an equation that establishes a relationship between two or more variables.

Analysis:

r(x) x s(x) = 2[tex]\sqrt{x}[/tex] x [tex]\sqrt{x}[/tex] = 2x

r2(4) = 2 x 4 = 8

r(x)/s(x) = 2[tex]\sqrt{x}[/tex]/ [tex]\sqrt{x}[/tex] = 2

In conclusion, the values of the product and quotient of the functions are 8 and 2 respectively.

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two dozen of pen cost rupee 60.find the cost of 25 such pens.​

Answers

Answer:

it costs rupee 3000 of 50 such pens

Explanation:

first, you have to multiply 50 x 60 which is 3000

second, two dozens of pens, right? so i add double 25 up which is 50 pens.

hope it helps and stay safe! (brainliest me pls)

The diagram shows a circle inside a square (16cm)
work out the area of the circle ​

Answers

The area of the circle inside the square shape is 200.96 cm²

How to determine the area of the circle?

The length of the square is given as:

L = 16 cm

This represents the diamater (d) of the circle.

The area of the circle is then calculated as:

Area = π(d/2)²

This gives

Area = 3.14 * (16/2)²

Evaluate

Area = 200.96

Hence, the area of the circle is 200.96 cm²

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Esther gave the storekeeper a twenty dollar bill for a purchase of $14.51. How
much change should she have received?

Answers

Answer:

She would have received $5.49 change

Answer:

$5.49 ~$5.50

Explanation: $20 - $15.51 = $5.49 therefore you have to round off which would initially equal to $5.50

Solve 10x + 16 2 6x + 20.
A. x29
B. x=9
c. x=1
D. x21


Answers

An equation is formed of two equal expressions. The value of x for which the equation has a solution is 1.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution for 10x+16=6x+20 is,

10x + 16 = 6x + 20

10x - 6x = 20 - 16

4x = 4

x = 1

Hence, the value of x for which the equation has a solution is 1.

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A wooden roller is 1 m long and 8 cm in diameter. Find it's mass in grams if 1cm³ of the wood has a mass of 0.7 g​

Answers

Answer:

1120π grams

==> 3518.58 grams  using value of π = 3.14159 or

==> 3520 grams using value of π = 22/7

Step-by-step explanation:

Volume of a cylinder = πr²l where r is the radius of the base and h is the length of cylinder

The diameter of the cylinder, d = 8cm and radius = d/2 = 4cm

Length = 1 meter = 100 cm

Here, volume V = π.4².100 =  π x 16 x 100 = 1600π cm³

Since 1 cm³ has a mass of 0.7gm total mass
M = 0.7V = (0.7)1600π =1120π gm


Using the ratio 22/7 for pi we get
M =  1120 x 22/7  = 3520 g

If we use the more accurate value of π as 3.14159 then we get
M = 1120 x 3.14.159 = 3518.58 g which is more accurate

please help please help​

Answers

Answer:

angleEAF=angleBAC (शिर्षभिमुख कोण भएर)

10x+90+5x=180 (सरल कोण भएर)

or, 15x+90=180

or, 15x=180-90

or, 15x=90

or, x=90÷15

or, x=4

Answer:

x=6

Step-by-step explanation:

90°+5x+10x=180°

90°+15x=180°

15x=180°-90°

15x=90°

x=90/15

=6

10×6=60

5×6=30

60°+30°=90°

90°+90°=180°

x=6 QED

f(x)=x^5+(x+3)^2 which value completed the table

Answers

Answer:

three boys shared D 10,500.00 in the ratio 6:7:8.find the largest share.

For each of the descriptions below, create a system of linear inequalities (please help will mark brainliest for whoever answers correctly!)

Answers

Answer:

hope you can understand

What is the volume of this rectangular
pyramid?
3 m
4 m
Submit
5 m
cubic meters

Answers

Given:l= 5 meterb= 4 meterh= 3 meterNote that:l= length b= breadth h= height To find:

The volume of the given rectangular pyramid.

Solution:

[tex]\large\boxed{Formula:V=\frac{1}{3}lbh}[/tex]

First, multiply the length (5), breadth (4) and height (3).

[tex]5×4×3[/tex]

[tex]= 60 \: cm [/tex]

Now, divide 60 by 3.

[tex]\frac{60}{3}[/tex]

[tex]\large\boxed{V= 20 \: {m}^{3}}[/tex]

Therefore, the volume of the given rectangular pyramid is 20 cubic meters.

Now explore a few more-difficult problems.
Which of the following statements are true for all the
problems?
The first step is always to divide.
○ The last step is always to subtract.
The decimal always moves one place to the right.
The next to last step is always to multiply.

Answers

The statement that is true for all the problems is " The last step is always to subtract.". Option B.  This is further explained below.

What is Arithmetic?

Generally, Arithmetic is simply defined as the area of mathematics concerned with the study and manipulation of numbers and their properties.

In conclusion, "The final step is always to subtract." is the universally true solution to the difficulties.

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Answer: B & D

Step-by-step explanation: I did this assignment.

A ball is thrown into the air with an initial velocity of 80 ft/sec. The height of the ball after t seconds in the air is given by h(t) = -16t? + 80t + 96. When will the ball be at its
highest point? Show all work.

Answers

Check the picture below.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+80}t\stackrel{\stackrel{c}{\downarrow }}{+96} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 80}{2(-16)}~~~~ ,~~~~ 96-\cfrac{ (80)^2}{4(-16)}\right) \implies \left( - \cfrac{ 80 }{ -32 }~~,~~96 - \cfrac{ 6400 }{ -64 } \right) \\\\\\ \left(\cfrac{5}{2}~~,~~96+100 \right)\implies \stackrel{highest~point}{\stackrel{\qquad ~~ \downarrow }{\left(2\frac{1}{2}~~,~~196 \right)}}[/tex]

Please solve with explanation (high points)

Answers

Answer:

see the attachment photo!

translate the question into an equation. Do not solve. Let n be the unknown number. what is 1% of 77?​

Answers

Answer:

1% × 77 = n

I used multiplication since "of" counts as multiplication.

For the arithmetic sequence beginning with the terms (11, 17, 23, 29, 35), what is the sum of
the first 17 terms?

a.) 1116
b.) 1003
c.) 1235
d.) 896

Answers

Option B is the correct answer.

The sum of 17 terms of the given arithmetic sequence is 1003.

What is Arithmetic Sequence?

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.

Here, given sequence :

  11, 17, 23, 29, 35, ......

first term a = 11

common difference d = 17 - 11 = 6

n = 17

Sₙ = n/2 {2a + (n-1)d}

S₁₇ = 17/2 { 2 X 11 + (17-1)X6}

S₁₇ = 17/2 { 22 + 16 X 6}

S₁₇ = 17/2 X 118

S₁₇ = 17 X 59

S₁₇ = 1003

Thus, the sum of 17 terms of the given arithmetic sequence is 1003.

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which inequality is represented by the graph

Answers

Answer:

This is your teacher if you do this again, I will contact your parents and you will get in big trouble.

Step-by-step explanation:

2 ³✓3 × 3✓2 please answer this fast

Answers

[tex]2\sqrt[3]{3} \cdot 3\sqrt 2\\\\=6 \cdot \sqrt[3]{3} \cdot \sqrt 2\\\\=6\cdot 3^{\tfrac 13} \cdot 2^{\tfrac 12}\\\\\approx 12.24[/tex]

12.24
Hopefully this helps

In the number 9,206.457138, what is the value of 1?​

Answers

Answer:

0.0001 or 1/10000 or 1 ten thousandths

Step-by-step explanation:

The 1 is 4 places after the decimal point so has a value of :

0.0001 or 1/10000 or 1 ten thousandths

Hope this helped and have a good day

What is the surface area of this 3d character based off the illustration. Can you provide explanation. Thank you.

Answers

The surface area of this 3d character based off the illustration will be 289.

How to explain the surface area?

It should be noted that the surface area simply means the amount of space that covers the outside of a shape.

Here the length of the shape is 17 and the width is also 17 as well. It should be noted that the width and length are determined by looking at the axis of the shapes drawn.

In this case, the area will be:

Length × Width

= 17 × 17

= 289

In conclusion, the surface area is 289.

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