Solve for X | Calculate Area of the Blue Trapezoid | Trapezium | Important Geometry skills explained

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Solve for X | Calculate Area of the Blue Trapezoid | Trapezium | Important Geometry skills explained

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[JSSTyger]

A triangle can be generated where (2x+2)² = (x+4)²+(x+2)² and x can be solved for. After that, the formula for trapezoid area can be used.

[mohanramachandran]

Very interesting sum & nice solutions
Thanks

[bigm]

Thanks, Professor, for another fabulous solution!❤🥂

[MichaelWillems]

Straightforward.
To solve the quadratic equation, why not use the standard x = (-b ± √ (b2 - 4ac) )/2a ?

[HappyFamilyOnline]

Great explanation👍
Thanks for sharing😊

[alittax]

Thank you for this excellent video! I've done a couple of things differently. I'll share my solution for anyone interested.

1:44 The equation I wrote was

a + x + 1 = 2x + 3

because the base of the triangle is = a.

From the above we get

a = x + 2

4:30 I factored the 2. So my equation is

2 * (x + 2) * (x - 4) = 0

Which means that either

x = -2

or

x = 4.

Since a side's length must be a positive number, we know that x = 4.

[alster]

After seeing the thumbnail, I solved it on my own and got the same answer.

Very easy.

[wackojacko]

A Scalene Trapezoid...a non isosceles Trapezoid with no sides congruent (of equal length)....my favorite. A perfect example that anything is possible in the real world...don't reject results.🙂

[devondevon]

x=4
Draw a perpendicular line from the top forming a right- triangle and a rectangle, x+4 by x+1
Two sides of the triangle are 2x+2 and x+4. The third side is (2x+3) - (x+1) = x+2; hence
(2x + 2)^2 - (x+4)^2 =(x+2)^2 [ Pythagorean )
4x^2+8x+4 - (x^2 + 8x + 16) = x^2+4x+4
3x^2 -12 = x^2 +4x+4
2x^2 -4x -16 =0
x^2 -2x- 8 = 0 (Divide both sides by 2)
(x-4)(x+2) = 0
x=4 and x=-2
Hence x =4 Answer

[shadmanhasan]

We can devide side AB -> "a" and "b"
-> b = (x+1) and a = (x+2) -> Trapazoid ABCD can be broken into 2 parts:
Rectangle DCb -> (x+1)(x+4) = x^2+5x+4
Triangle ADa -> [(x+2)(x+4)]/2
= (x^2+6x+8)/2 -> using handy-dandy Desmos: DCb = f(x) and ADa = g(x)
Letting area = f(x) + g(x) -> leading to 2 roots: (-4, 0), (-4/3, 0). Dunno how to carry this on guys, do i need to differentiate?
If that's the case, let h(x)=f(x)+g(x) = 3/2x^2+8x+8 -> h'(x)=3x+8
Damn, forgot abt Pythagoras Theorem 😂

[santiagoarosam]

AB=(x+2)+(x+1) → (2x+2)² - (x+2)² =(x+4)² → x=4 → DC=5 ; AB=11 ; CB=8 → Área azul = [(11+5)/2]*8 =64
Gracias y saludos.

[quigonkenny]

Let E be the point on AB such that DE is perpendicular to AB. As EBCD is a rectangle, BC = DE and CD = EB.

AE = AB - EB
AE = (2x+3) - (x+1) = x + 2

Triangle ∆AED:
a² + b² = c²
(x+2)² + (x+4)² = (2x+2)²
x² + 4x + 4 + x² + 8x + 16 = 4x² + 8x + 4
2x² + 12x + 20 = 4x² + 8x + 4
2x² - 4x - 16 = 0
x² - 2x - 8 = 0
(x-4)(x+2) = 0
x - 4 = 0 | x + 2 = 0
x = 4 ✓ | x = -2 ❌

Trapezoid ABCD:
A = h(a+b)/2
A = (x+4)(x+1+2x+3)/2
A = (x+4)(3x+4)/2
A = (4+4)(12+4)/2
A = 8(16)/2 = 64

[yamunaravi]

I got the same answer using the same method

[vidyadharjoshi]

Draw a perpendicular DE to AB. (X+4)sq + (X+2)sq = (2X+2)sq. Solve for X. X = 4.
Area of trapezoid = 0.5*(a+b)*h = 0.5*(5+11)*8 = 64

[williamwingo]

No peeking, no calculator. Did it pretty much the same way except using the quadratic formula, so I won't repeat the details.

[kcp-Kmoons]

Before I watch I solve to find the area of trapezoid ABCD:

B¹=5
B²=11
Diagonal=10
Height=8
B²-B¹=6

x=4
Area=64 square units

[TheTiberius]

Ok. That was a bit boring. Love your channel though! No disrespect for anyone who had to think this through more than x times time. I am older. Your channel keeps my mental health in a. Good state of mind.

[ybodoN]

Since the trapezoid was divided to find x, its area is ½ (x + 2) (x + 4) + (x + 1) (x + 4).
(so no worries in case you don't remember the formula for the area of a trapezoid…)