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Let The Real Beauty With Brain Show Themselves (mr Shape) - Education - Nairaland

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Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 7:29pm On Apr 24, 2019
Show your maths skills

Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 8:41pm On Apr 24, 2019
Please show your workings not just answers
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 10:13pm On Apr 24, 2019
Anyone?
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by Martinez39(m): 11:28pm On Apr 24, 2019
Shapes are getting tougher.
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 11:41pm On Apr 24, 2019
Martinez39:
Shapes are getting tougher.
Lol, then we are getting stronger,

Don't worry by tomorrow I will be post one with difficulty low and another high.
But let's kill this first sir
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by Martinez39(m): 2:39am On Apr 25, 2019
grin

15.1948232 units².

Let me cross-check, I will post my workings soon.
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by Martinez39(m): 4:00am On Apr 25, 2019
NB: I don't know basic geometry too well like ifada123 so I used coordinate geometry.

1) Place the diagram on a rectangle coordinate plane such that A is at the origin and AB lies on the positive x-axis. Finally let θ be the angle ∠EAF

2) Using θ, we have the coordinates of all points :
A(0, 0), E(4Cosθ, 4Sinθ), D(7Cosθ, 7Sinθ), C(7Cosθ + 3, 7Sinθ) & B(7Cosθ + 3, 0). The coordinates for F isn't given.

3) Using the aforementioned coordinates, the slope of the line through EC is
m = Sinθ/(1 + Cosθ)
The line through EF is perpendicular to the line through EC and hence has a slope
m' = -(1 + Cosθ)/Sinθ
Using the slope-point form, the equation of the line through EF is
(y - 4Sinθ) = [-(1 + Cosθ)/Sinθ](x - 4Cosθ) ---- (1)
The x-intercept of this line would give you the x-coordinate of F. Making y = 0 in (1), we have x = 4.
Therefore F is the point (4, 0)

4) Using the coordinates of point B and F, we have
(7Cosθ + 3) - 4 = 5.
Therefore Cosθ = 6/7. We have Sinθ = (√13)/7
Using this, we can evaluate the coordinates of points B, C, F and E. Doing this, we have
B(9, 0), C(9, √13), F(4, 0) & E( 24/7, (4√13)/7)

5) The area of the required region is the sum of the areas of EFC and CFB. Using these coordinates together with the distance formula,
EFC = ½(|EF|)(|EC|) = (2√22932)/49
CFB = ½(|CB|)(|BF|) = (5√13)/2
EFC + CFB = ( (5√13)/2 ) + ( (2√22932)/49 ) ≈ 15.1948232 units².

The area is 15.1948232 units².
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by Martinez39(m): 4:20am On Apr 25, 2019
@ifada123

I am getting busy recently and may not participate in the challenges as frequently. Still keep the shapes coming. Your work is appreciated.
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by femi4: 8:07am On Apr 25, 2019
cry
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by shegzy2009: 8:59am On Apr 25, 2019
24.5 sq. units.
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by Nobody: 1:52pm On Apr 25, 2019
ifada123:
Show your maths skills
are u a teacher
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 3:50pm On Apr 26, 2019
Martinez39:
NB: I don't know basic geometry too well like ifada123 so I used coordinate geometry.

1) Place the diagram on a rectangle coordinate plane such that A is at the origin and AB lies on the positive x-axis. Finally let θ be the angle ∠EAF

2) Using θ, we have the coordinates of all points :
A(0, 0), E(4Cosθ, 4Sinθ), D(7Cosθ, 7Sinθ), C(7Cosθ + 3, 7Sinθ) & B(7Cosθ + 3, 0). The coordinates for F isn't given.

3) Using the aforementioned coordinates, the slope of the line through EC is
m = Sinθ/(1 + Cosθ)
The line through EF is perpendicular to the line through EC and hence has a slope
m' = -(1 + Cosθ)/Sinθ
Using the slope-point form, the equation of the line through EF is
(y - 4Sinθ) = [-(1 + Cosθ)/Sinθ](x - 4Cosθ) ---- (1)
The x-intercept of this line would give you the x-coordinate of F. Making y = 0 in (1), we have x = 4.
Therefore F is the point (4, 0)

4) Using the coordinates of point B and F, we have
(7Cosθ + 3) - 4 = 5.
Therefore Cosθ = 6/7. We have Sinθ = (√13)/7
Using this, we can evaluate the coordinates of points B, C, F and E. Doing this, we have
B(9, 0), C(9, √13), F(4, 0) & E( 24/7, (4√13)/7)

5) The area of the required region is the sum of the areas of EFC and CFB. Using these coordinates together with the distance formula,
EFC = ½(|EF|)(|EC|) = (2√22932)/49
CFB = ½(|CB|)(|BF|) = (5√13)/2
EFC + CFB = ( (5√13)/2 ) + ( (2√22932)/49 ) ≈ 15.1948232 units².

The area is 15.1948232 units².
Try again sir

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Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 3:50pm On Apr 26, 2019
shegzy2009:
24.5 sq. units.
Try again sir
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 3:51pm On Apr 26, 2019
Sorry I reply late
Let's keep the workings coming
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by Martinez39(m): 4:17pm On Apr 26, 2019
ifada123:

Try again sir
Nice to have you back. Show us your working. This question don all of us strong thing.
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 7:16pm On Apr 26, 2019
Martinez39:
Nice to have you back. Show us your working. This question don all of us strong thing.
Ok sir
I will prepare solution soon,
If get home.
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by shegzy2009: 7:58pm On Apr 26, 2019
ifada123:

Try again sir
Chai....This is serious.
Pls show us your solution.
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by Martinez39(m): 10:08am On Apr 27, 2019
ifada123:

Ok sir
I will prepare solution soon,
If get home.
We are waiting.
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 12:16pm On Apr 27, 2019
Martinez39:
NB: I don't know basic geometry too well like ifada123 so I used coordinate geometry.

1) Place the diagram on a rectangle coordinate plane such that A is at the origin and AB lies on the positive x-axis. Finally let θ be the angle ∠EAF

2) Using θ, we have the coordinates of all points :
A(0, 0), E(4Cosθ, 4Sinθ), D(7Cosθ, 7Sinθ), C(7Cosθ + 3, 7Sinθ) & B(7Cosθ + 3, 0). The coordinates for F isn't given.

3) Using the aforementioned coordinates, the slope of the line through EC is
m = Sinθ/(1 + Cosθ)
The line through EF is perpendicular to the line through EC and hence has a slope
m' = -(1 + Cosθ)/Sinθ
Using the slope-point form, the equation of the line through EF is
(y - 4Sinθ) = [-(1 + Cosθ)/Sinθ](x - 4Cosθ) ---- (1)
The x-intercept of this line would give you the x-coordinate of F. Making y = 0 in (1), we have x = 4.
Therefore F is the point (4, 0)

4) Using the coordinates of point B and F, we have
(7Cosθ + 3) - 4 = 5.
Therefore Cosθ = 6/7. We have Sinθ = (√13)/7
Using this, we can evaluate the coordinates of points B, C, F and E. Doing this, we have
B(9, 0), C(9, √13), F(4, 0) & E( 24/7, (4√13)/7)

5) The area of the required region is the sum of the areas of EFC and CFB. Using these coordinates together with the distance formula,
EFC = ½(|EF|)(|EC|) = (2√22932)/49
CFB = ½(|CB|)(|BF|) = (5√13)/2
EFC + CFB = ( (5√13)/2 ) + ( (2√22932)/49 ) ≈ 15.1948232 units².

The area is 15.1948232 units².
You maybe right
I later found out my solution is inconsistent with geometry theorem.
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 12:19pm On Apr 27, 2019
I think the question requires more details,
I just got the Shape, maybe there are more write up to it.
Sorry for the delay,
Further light gotten will be communicated
To you guys
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by Martinez39(m): 12:21pm On Apr 27, 2019
ifada123:

You maybe right
I later found out my solution is inconsistent with geometry theorem.
Yeah. I was surprised when you said that I was incorrect because I exhaustively checked my workings.

1 Like

Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 12:25pm On Apr 27, 2019
Tumbs up,
Look forward to the next shape,
I am posting now
Re: Let The Real Beauty With Brain Show Themselves (mr Shape) by ifada123: 8:30am On Apr 28, 2019
Martinez39:
NB: I don't know basic geometry too well like ifada123 so I used coordinate geometry.

1) Place the diagram on a rectangle coordinate plane such that A is at the origin and AB lies on the positive x-axis. Finally let θ be the angle ∠EAF

2) Using θ, we have the coordinates of all points :
A(0, 0), E(4Cosθ, 4Sinθ), D(7Cosθ, 7Sinθ), C(7Cosθ + 3, 7Sinθ) & B(7Cosθ + 3, 0). The coordinates for F isn't given.

3) Using the aforementioned coordinates, the slope of the line through EC is
m = Sinθ/(1 + Cosθ)
The line through EF is perpendicular to the line through EC and hence has a slope
m' = -(1 + Cosθ)/Sinθ
Using the slope-point form, the equation of the line through EF is
(y - 4Sinθ) = [-(1 + Cosθ)/Sinθ](x - 4Cosθ) ---- (1)
The x-intercept of this line would give you the x-coordinate of F. Making y = 0 in (1), we have x = 4.
Therefore F is the point (4, 0)

4) Using the coordinates of point B and F, we have
(7Cosθ + 3) - 4 = 5.
Therefore Cosθ = 6/7. We have Sinθ = (√13)/7
Using this, we can evaluate the coordinates of points B, C, F and E. Doing this, we have
B(9, 0), C(9, √13), F(4, 0) & E( 24/7, (4√13)/7)

5) The area of the required region is the sum of the areas of EFC and CFB. Using these coordinates together with the distance formula,
EFC = ½(|EF|)(|EC|) = (2√22932)/49
CFB = ½(|CB|)(|BF|) = (5√13)/2
EFC + CFB = ( (5√13)/2 ) + ( (2√22932)/49 ) ≈ 15.1948232 units².

The area is 15.1948232 units².
U are correct
I will bring a basic shape solution to it soon,

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