Find the volume of the following cone

find the area of the trapezium whose parallel sides are 25 cm and 13 cm The Other sides of a Trapezium are 15 cm and 15 CM

Snezhnost [94]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - A trapezium ABCD with non parallel sides of measure 15 cm each ! along , the parallel sides are of measure 13 cm and 25 cm

To find - Area of trapezium

Refer the figure attached ~

In the given figure ,

AB = 25 cm

BC = AD = 15 cm

CD = 13 cm

Construction -

$draw \: CE \: \parallel \: AD \: \\ and \: CD \: \perp \: AE$

Now , we can clearly see that AECD is a parallelogram !

$\therefore$ AE = CD = 13 cm

Now ,

$AB = AE + BE \\\implies \: BE =AB - AE \\ \implies \: BE = 25 - 13 \\ \implies \: BE = 12 \: cm$

Now , In ∆ BCE ,

$semi \: perimeter \: (s) = \frac{15 + 15 + 12}{2} \\ \\ \implies \: s = \frac{42}{2} = 21 \: cm$

Now , by Heron's formula

$area \: of \: \triangle \: BCE = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies \sqrt{21(21 - 15)(21 - 15)(21 - 12)} \\ \implies \: 21 \times 6 \times 6 \times 9 \\ \implies \: 12 \sqrt{21} \: cm {}^{2}$

Also ,

$area \: of \: \triangle \: = \frac{1}{2} \times base \times height \\ \\\implies 18 \sqrt{21} = \: \frac{1}{\cancel2} \times \cancel12 \times height \\ \\ \implies \: 18 \sqrt{21} = 6 \times height \\ \\ \implies \: height = \frac{\cancel{18} \sqrt{21} }{ \cancel 6} \\ \\ \implies \: height = 3 \sqrt{21} \: cm {}^{2}$

Since we've obtained the height now , we can easily find out the area of trapezium !

$Area \: of \: trapezium = \frac{1}{2} \times(sum \: of \:parallel \: sides) \times height \\ \\ \implies \: \frac{1}{2} \times (25 + 13) \times 3 \sqrt{21} \\ \\ \implies \: \frac{1}{\cancel2} \times \cancel{38 }\times 3 \sqrt{21} \\ \\ \implies \: 19 \times 3 \sqrt{21} \: cm {}^{2} \\ \\ \implies \: 57 \sqrt{21} \: cm {}^{2}$

hope helpful :D

6 0

2 years ago

Possible solution for 4+x+2-2x=5

MrRissso [65]

Answer:

x=1

Step-by-step explanation:

For algebra always start by rewriting it.

4+x+2-2x=5

Then ask yourself is there any like terms we can combine, and here yes there is. 4 and 2 and x and -2x. Now lets combine them and rewrite.

6-x=5

Now lets get x alone and the quickest way is to subtract 6 to the other side

6-x=5

-6 -6

-x=-1

Now the two negatives cancel out as you would divide both sides by the coefficient -1 to get positive x alone. We can make this easier by just canceling out the negatives.

Your answer is

x=1

3 0

3 years ago

My first ever question on this site. Hope i will get my answer as i have answer others.

Neko [114]

632=.60 x (it is important to convert the percentage to decimal by dividing by 100)
632/.60=x
x= 1053.33
x is your original price
the actual answer is 1053.3333(3 repeating) but since it is money you cut it off at 2 decimal points.

6 0

3 years ago

Read 2 more answers

A man divided $9,000 among his wife, son, and daughter. The wife received twice as much as the daughter, and the son received $1

monitta

Answer:

Q1:

Share of the daughter (x):

2x + x + x + $1,000 = $9,000

4x = $8,000

x = $2,000

Share of the wife:

= 2($2,000)

= $4,000

Share of the son:

= $2,000 + $1,000

= $3,000

Answer: wife, $4,000; son, $3,000; daughter, $2,000

Q2:

= 1/2x + $1,000

Answer: 1/2x + $1,000: expression for share of the son

Proof (the wife shares $4,000):

Share of wife (x):

x + 1/2x + 1/2x + $1,000 = $9,000

2x = $8,000

x = $4,000

Step-by-step explanation:

hope it helps!

6 0

3 years ago

A cars value starts at $32,000. After 1 year, it is worth $27,200. What is the decay factor?

notka56 [123]

Answer:

15% × 7 = 1.05

32,000 - 1.05 = 31,998.95

31,998.95 ‐‐‐‐‐> 31,999

$31,999

(If you don't need to simplify, the answer would be $31,998.95, but I did it just incase you do)

Step-by-step explanation:

7 0

3 years ago