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vazorg [7]
3 years ago
15

Find the area of the kite.

Mathematics
1 answer:
Alchen [17]3 years ago
8 0

Answer:

72

Step-by-step explanation:

One way to do this is to use the formula  A=\frac{1}{2}d_1 d_2  where d_1 and d_2 are the lengths of the two diagonals.

In the figure, d_1=12  and  d_2=12  (2 + 10 and 6 + 6).

The area is \frac{1}{2}(12)(12)=\frac{1}{2}144=72 square units.

Another way that doesn't depend on learning a formula is to remember that the diagonals of a kite are perpendicular, so the 4 small triangles are right triangles.  Two of the smaller triangles have base =2 and height = 6, so their areas are 1/2(2)(6) = 6.  Double that--there are 2 congruent small triangles--to get an area of 12.

There are two larger right triangles with base =10 and height = 6, so their area are 1/2(10)(6)=30.  There are two of those, so their combined area is 60.

Finally, put the small triangle area and the large triangle area together to get a total of 12 + 60 = 72

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There are 30 students in a class. Which equations represent the situation if the number of boys
aalyn [17]

Step-by-step explanation:

A. b x 30 = 7E. b x 7 =30C. b = 30 + 7

3 0
3 years ago
Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 181.5 square cen
3241004551 [841]

Answer:

The base and height of the solid is 5.5cm

<em></em>

Step-by-step explanation:

Given

Surface\ Area = 181.5cm^2

Required

Determine the dimensions that maximizes the volume

Let the base dimension be x and the height be h

The volume is calculated as:

Volume =x^2 * h

Volume =x^2h

181.5 =x^2h

The surface area (S) is calculated as this:

S = 2(x^2 + xh + xh)

S = 2(x^2 + 2xh)

S = 2x^2 + 4xh

Substitute 181.5 for S

181.5 = 2x^2 + 4xh

Make h the subject:

4xh = 181.5 - 2x^2

h = \frac{181.5 - 2x^2}{4x}

Substitute h = \frac{181.5 - 2x^2}{4x} in Volume =x^2h

V = x^2(\frac{181.5 - 2x^2}{4x})

V = x(\frac{181.5 - 2x^2}{4})

V = \frac{1}{4}(x)(181.5 - 2x^2)

V = \frac{181.5x}{4} - \frac{2x^3}{4}

V = \frac{181.5x}{4} - \frac{x^3}{2}

To get the maximum, we differentiate V with respect to t and set the differentiation to 0

dV = \frac{181.5}{4} - \frac{3x^2}{2}

Set to 0

0 = \frac{181.5}{4} - \frac{3x^2}{2}

\frac{3x^2}{2} = \frac{181.5}{4}

Multiply through by 4

4 * \frac{3x^2}{2} = \frac{181.5}{4} * 4

2*3x^2 = 181.5

6x^2 = 181.5

x^2 = \frac{181.5}{6}

x^2 = 30.25

x = \sqrt{30.25

x = 5.5

Recall that:

h = \frac{181.5 - 2x^2}{4x}

h = \frac{181.5 - 2 * 5.5^2}{4 * 5.5}

h = \frac{181.5 - 60.5}{22}

h = \frac{121}{22}

h = 5.5

So, we have:

h = 5.5

x = 5.5

<em>Hence, the base and height of the solid is 5.5cm</em>

7 0
4 years ago
A number plus itself, plus twice itself, plus 4 times itself is equal to -104
NARA [144]

The scenario will will be represented by: x+x+2x+4x=-104

The number will be -13

Step-by-step explanation:

We have to convert the given situation into the mathematical form

Let x be the number

Then

"a number plus itself"

x+x

"plus twice itself"

x+x+2x

"plus 4 times itself"

x+x+2x+4x

"is equal to -104"

x+x+2x+4x=-104

This can also be written as:

x+x+2x+4x=-104\\8x=-104\\Dividing\ both\ sides\ by\ 8\\\frac{8x}{8}=\frac{-104}{8}\\x=-13

Keywords: Linear Equation

Learn more about linear equation at:

  • brainly.com/question/2150928
  • brainly.com/question/2154850

#LearnwithBrainly

7 0
3 years ago
If the volume of a sphere is 36pi cubic units, what is the radius?
prisoha [69]
The radius is about 2.05
6 0
4 years ago
Read 2 more answers
What is 7÷10 in faction form and improper fraction form ​
leonid [27]

Answer:

a) 7/10

b) There is no improper fraction form for this

5 0
3 years ago
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