Can you find area of the Green shaded region? | (Think outside the Box) | #math #maths | #geometry

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Can you find area of the Green shaded region? | (Think outside the Box) | #math #maths | #geometry

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[yalchingedikgedik]

Thanks Sir
That’s very well
A wonderful method of solution
We are learning more from like these exercises
With glades
❤❤❤❤❤

[scottdort]

Rectangle up the boundary to a 7 x 15 box. Area is 105 units.
Top triangle is 42 units.
Bottom triangle is 15 units.
Top left rectangle is 12 units.
Subtract to 3 values from 105 and you get 36 units.
Premath, I love you but sometimes your solutions are a bit overly complicated but keep in mind, I am an engineer.

[kevi]

Divide the green area into 3 triangles. First has a base of 3and height 3 hence area is 4.5. The second has a base of 5 and height 3 hence area 7.5 the third has a base of 4 and height 12 hence area 24. Combined area is 4.5 + 7.5 + 24 = 36. This is surely simpler !

[gaylespencer]

Approached it differently. GET the area of the big triangle, 7 times 12 divided by 2 = 42.
Then REMOVE from that 42 the area of white triangle in the lower left of the middle square: (2.1)(7)/2 = (7.35).
Then ADD to that that net area the area of the green triangle in the lefthand square: (.9)(3)/2=1.35
Total, 42 minus 7.35 plus 1.35 = 36

Getting the 2.1 was done by trig. Arctan 3/10 = 16.699... degrees Then use the tangent function of that angle to get the height of this white triangle, tan(16.999...) times 7 = 2.1

[phungpham]

1/ From F drop FH perpendicular to the base BD
We have: side of the biggest square = 7
Area of the green area= (area of the smallest square+area of triangle FHD)- area of triangle ABC = (9+42)-15= 36 sq units😊

[santiagoarosam]

b=3+3+4+5=15; h=7---> bh=105---> Área sombreada
Gracias y saludos.

[uuxejfk]

triangle and trapezoid. 1/2(4*12)+1/2(3+5)*3=24+12=36

[xhkeryu]

No constructions, simply


3² + ½x12x7 - ½x10x3 = 36

[pedllz]

.... just the big triangle 7x12/2 plus the 3x3 square minus the small triangle 10x3/2

[-wx--]

Overlay a 1×1 grid, then use Pick's theorem: inner points i=30, boundary points b=14, area A = i+b/2−1 = 30+7−1 = 36. 😉

[quigonkenny]

Vertex labeling:
Middle square, clockwise from top left: A, B, C, D
Left square, clockwise from bottom right: D, E, F, G
Right square, clockwise from bottom left: C, H, J, K

Extend EF and BA and have them intersect at M. Extend KJ and AB and have them intersect at N. As MN and KE are parallel and EM and NK are parallel and ∠JKC = ∠DEF = 90°, MNKE is a rectangle. The green area is going to be equal to the area of MNKE minus the areas of the triangles ∆CEF and ∆ANK and the rectangle FMAG.

The left square side length is given as 3. As GA = 4, the middle square side length is 4 + the left side length, 4+3 = 7. The right square side length is given as 5.

Thus EF = 3, CE = 7+3 = 10, AN = 7+5 = 12, NK = DM = 7, and MN = KE = 3+7+5 = 15.

Green area:
Aɢ = Aᴍɴᴋᴇ - Aꜰᴍᴀɢ - Aᴄᴇꜰ - Aᴀɴᴋ
Aɢ = 7(15) - 4(3) - 10(3)/2 - 12(7)/2
Aɢ = 105 - 12 - 15 - 42 = 105 - 69 = 36 sq units

[Waldlaeufer]

Triangle in the square on the right (square 3):
A = 1/2 * 5 * 7/12 * 5 = = 35/24 * 5 = 175/24
Trapezoid in the middle square:
h = 7/12 * 5 = 35/12
A = 1/2 (4 + 35/12) * 7 = (2 + 35/24) * 7 = (48/24 + 35/24) * 7 = 83/24 * 7 = 581/24
Triangle in the bottom of squares 1 and 2:
A = 1/2 * 3 * 3 = 9/2

Total green area:
A(green) = 175/24 + 581/24 + 9/2 = 756/24 + 108/24 = 864/24 = 36 square units

[ChuzzleFriends]

The small square is connected to the large one, so the side length of the large square is 3 + 4 = 7 units by the Segment Addition Postulate.
Raise the middle square to be the height of the large one (Don't change the length). This creates a new rectangle with length 5 and width 7 (and fully completes another triangle). When we combine this rectangle with the large square, we get a large rectangle with length 12 and width 7.
Green Region Area = Small Square Area + Large Rectangle Area - Bottom Triangle Area - Top Triangle Area.
Both triangles are right triangles by definition of rectangles.
By the Segment Addition Postulate, the base of the bottom triangle is 3 + 7 = 10 units.
Likewise, the base of the top triangle is 7 + 5 = 12.
A = s²
= 3²
= 9
A = lw
= 12 * 7
= 84
A = (bh)/2
= 1/2 * 3 * 10
= 3 * 5
= 15
A = 1/2 * 7 * 12
= 6 * 7
= 42
Green Region Area = 9 + 84 - 15 - 42
= 36
So, the area of the green shaded region is 36 square units.

[nandisaand]

I attacked this quite differently.
First, I found Z, which is the y-coordinate of the line AC where it crosses from Big Square to little square, with C (0, 0).
Slope of AC: (3/-10)=(-0.3)
Z=(-0.3)•X=(-0.3)•(-7)=2.1


=42+½[3•(3-2.1)]-½(7•2.1)
=42+1.35-7.35
=36

[giuseppemalaguti]

3:a=7:b, a+b=3..7a=3(3-a)..10a=9..a=9/10..b=21/10...Agreen=7*12/2+(9/10)*3/2-(21/10)*7/2=42+27/20-147/20=42-120/20=42-6=36

[SrisailamNavuluri]

There are 3 triangles with sides (7+5, 7), (3, 0.9)white small ∆ (7, 2.1)
Required area
=42+1/2(2.7-14.7)=42+1/2(-12)
=42-6=36 square units
I have taken 2 similar ∆les and height 3 of the square is divided into 2.1 and 0.9.(3:10=2.1:7)

[cristidan]

thank you for the video, waiting for more challenging ones! ♥♥♥

[MrPaulc]

Left to right, the boxes are 3*3, 7*7, 5*5.
Where the diagonal line crosses the right-hand side of the 3*3 box: it is 7/10 of the way across the left and middle boxes, so 7/10 of the way up the 3 side.
3*(7/10) = 2.1
Therefore, the largest part of the green area (outside the 3*3 box} is (7*12)/2 - (2.1*7)/2 = 42 - 7.35 = 34.65.
The green area inside the 3*3 box is (3*0.9)/2 = 1.35.
34.65 + 1.35 = 36 un^2
No need to go outside the box for this one.

[unknownidentity]

Let's find the area:
.
..
...
....


First of all we obtain the following side lengths (from the left to the right):

(1) 3
(2) 3+4=7
(3) 5

Now we draw the following auxiliary lines:

(A) Lower right corner of the middle square to the upper left corner of the middle square
(B) Lower right corner of the middle square to the upper right corner of the left square

These lines divide the green region into three triangles. Now we can calculate the area of the green region:

A = A₁ + A₂ + A₃ = (1/2)*3*3 + (1/2)*4*7 + (1/2)*5*7 = (9 + 28 + 35)/2 = 72/2 = 36

Best regards from Germany

[prossvay]

Connect to rectangle ABCD that Length=3+7+5=15
and Width=7
So rectangle area =(15)(7)=105 square units.
So area of green region= square units.❤❤❤