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2 years ago

What is the area of this polygon? 42. 5 units² 41. 5 units² 35. 5 units² 29. 5 units².

Mathematics

2 answers:

otez555 [7]2 years ago

8 0

Answer:

35.5 units^2

Step-by-step explanation:

Alona [7]2 years ago

7 0

The area of the polygon is 35.5 square units. Option C shows the correct area of the given polygon.

The area can be defined as the amount of space used by a two-dimensional object.

Given that ABEDFG is a polygon. As shown in the attachment, we divided the polygon into 4 different parts.

In triangle EDC, EC = 3, DC = 4.

Area = $\dfrac { 1}{2} \times EC \times DC$

Area = $\dfrac {1}{2} \times 3\times 4$

Area = 6

In triangle GFD, height = 2, base = 7.

Area = $\dfrac { 1}{2} \times base \times height$

Area = $\dfrac {1}{2} \times 2\times 7$

Area = 7

In triangle GDA, AD = 3, GD = 7.

Area = $\dfrac { 1}{2} \times AD \times GD$

Area = $\dfrac {1}{2} \times 3\times 7$

Area = 10.5

In rectangle ABCD, DC = AB = 4, CB = AD = 3.

Area = $AB\times AD$

Area = $4\times 3$

Area = 12

The area of the polygon is the sum of all the areas.

Area = 6 + 7 + 10.5 + 12

Area = 35.5 square units.

Hence we can conclude that the area of the polygon is 35.5 square units. Option C shows the correct area of the given polygon.

To know more about the area, follow the link given below.

brainly.com/question/1631786.

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Luda [366]

Answer:

w= -52

Step-by-step explanation:

We simplify the equation to the form, which is simple to understand

15-w/4=28

Simplifying:

15-0.25w=28

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-0.25w=+28-15

We simplify left and right side of the equation.

-0.25w=+13

We divide both sides of the equation by -0.25 to get w.

w= -52

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3 years ago

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3 years ago

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Yanka [14]

Answer:

$x=\frac{12}{7} \\y=\frac{12}{5} \\z=-12$

Step-by-step explanation:

Let's re-write the equations in order to get the variables as separated in independent terms as possible \:

First equation:

$\frac{xy}{x+y} =1\\xy=x+y\\1=\frac{x+y}{xy} \\1=\frac{1}{y} +\frac{1}{x}$

Second equation:

$\frac{xz}{x+z} =2\\xz=2\,(x+z)\\\frac{1}{2} =\frac{x+z}{xz} \\\frac{1}{2} =\frac{1}{z} +\frac{1}{x}$

Third equation:

$\frac{yz}{y+z} =3\\yz=3\,(y+z)\\\frac{1}{3} =\frac{y+z}{yz} \\\frac{1}{3}=\frac{1}{z} +\frac{1}{y}$

Now let's subtract term by term the reduced equation 3 from the reduced equation 1 in order to eliminate the term that contains "y":

$1=\frac{1}{y} +\frac{1}{x} \\-\\\frac{1}{3} =\frac{1}{z} +\frac{1}{y}\\\frac{2}{3} =\frac{1}{x} -\frac{1}{z}$

Combine this last expression term by term with the reduced equation 2, and solve for "x" :

$\frac{2}{3} =\frac{1}{x} -\frac{1}{z} \\+\\\frac{1}{2} =\frac{1}{z} +\frac{1}{x} \\ \\\frac{7}{6} =\frac{2}{x}\\ \\x=\frac{12}{7}$

Now we use this value for "x" back in equation 1 to solve for "y":

$1=\frac{1}{y} +\frac{1}{x} \\1=\frac{1}{y} +\frac{7}{12}\\1-\frac{7}{12}=\frac{1}{y} \\ \\\frac{1}{y} =\frac{5}{12} \\y=\frac{12}{5}$

And finally we solve for the third unknown "z":

$\frac{1}{2} =\frac{1}{z} +\frac{1}{x} \\\\\frac{1}{2} =\frac{1}{z} +\frac{7}{12} \\\\\frac{1}{z} =\frac{1}{2}-\frac{7}{12} \\\\\frac{1}{z} =-\frac{1}{12}\\z=-12$

8 0

3 years ago

Jenna has a garden with coordinate A(2,-1), B(4,3), C(9,3), D(7,-1) where each unit is 1 foot.

Sladkaya [172]

Answer:

a) The dimensions of the garden are: 4.5 ft and 5 ft

b) 22.5 ft² of fencing material

c) The most precise name for the shape of the garden is a Rectangle

Step-by-step explanation:

a) Jenna has a garden with coordinate A(2,-1), B(4,3), C(9,3), D(7,-1) where each unit is 1 foot.

What are the dimensions of the garden rounded to the nearest 10th? (Looking for the lengths of the sides)

When we are given coordinates, we find the dimensions using the formula

= √(x2 - x1)² - (y2 - y1)²

(x1 , y1) and (x2 - y2)

For side AB

A(2,-1), B(4,3)

= √(4 - 2)² + (3 - (-1))²

= √2² + 4²

= √4 + 16

= √20 units = √20 feet

= 4.472135955 feet

Approximately = 4.5 feet

For side BC

B(4,3), C(9,3)

= √(9 - 4)² + (3 - 3)²

= √5² + 0²

= √25

= 5 units = 5 feet

For side CD

C(9,3), D(7,-1)

= √(7 - 9)² + (-1 - 3)²

= √(-2)² + -4²

= √4 + 16

= √20 units = √20 feet

= 4.472135955 feet

Approximately = 4.5 feet

For side AD

A(2,-1), D(7,-1)

= √(7 - 2)² + (-1 - (-1))²

= √5² + (-1 + 1)²

= √5² + 0²

= √25

= 5 units = 5 feet

Therefore, the dimensions of the garden are: 4.5ft and 5 ft

b) If Jenna decides to buy fencing for the garden, how much fence material does she need to buy? (Free response)

To buy fencing material for the garden, we have to find the area of the garden

Formula = Length × Width

= 4.5 ft × 5 ft

= 22.5 ft²

Therefore, Jenna needs to buy 22.5 square feet of fencing material.

c) What is the most precise name for the shape of the garden?

From the above calculation, we can see that

Side AB = Side CD = 4.5 ft

Side BC = Side AD = 5 ft

Therefore, the most precise name for the shape of the garden is a Rectangle

6 0

3 years ago