Two Methods! | Calculate area of the Green Rectangle | (Rectangle areas) | #math #maths

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Two Methods! | Calculate area of the Green Rectangle | (Rectangle areas) | #math #maths

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[unknownidentity]

Merry Christmas to the whole PreMath community.

And now let's find the green area:
.
..
...
....


Let x and y be the labels of the horizontal and vertical side length, respectively. Then we have:

x(pink) = 3
y(pink) = A(pink)/x(pink) = 7/3

y(white) = y(pink) = 7/3
x(white) = A(white)/y(white) = 8/(7/3) = 24/7

x(blue) = x(pink) + x(white) = 3 + 24/7 = 21/7 + 24/7 = 45/7
y(blue) = A(blue)/x(blue) = 15/(45/7) = 7/3

y(yellow) = y(white) + y(blue) = 7/3 + 7/3 = 14/3
x(yellow) = A(yellow)/y(yellow) = 26/(14/3) = 39/7

x(green) = x(white) + x(yellow) = 24/7 + 39/7 = 9
y(green) = 8 − y(yellow) = 8 − 14/3 = 24/3 − 14/3 = 10/3
A(green) = x(green)*y(green)= 9*10/3 = 30

Best regards from Germany

[kennethstevenson]

Found missing dimensions by dividing each are by the known dimension starting with 3 area 7 to get 7/3. the answer was found by solving A = 10/3 X [ (26x 13/4) + 24/7 ] = 10/3 x 9 = 30 square units.

[prossvay]

Let a is Length of rectangle and b is width
(8-b)(3)=14
24-3b=14
3b=24-14=10
b=10/3 units
8+8+26=a(8-10/3)
14a/3=42
14a=126
a=126/14=9units
Area of the green rectangle=(10/3)(9)=30 square units. Thanks ❤❤❤

[ИванПоташов-ою]

8*3-7-7=10 - the area of "missing" part. Area/42=10/14. So, Area=30.

[yalchingedikgedik]

Thanks Sir
That’s very useful and enjoyable 2 methods
With glades
❤❤❤❤❤

[MrPaulc]

I will try winging this one: Split the blue rectangle vertically. As it has the same width as grey and white combined, and the same area, it also has the same height. Grey plus left side of blue have a combined area of 14, so a height of 14/3 (due to the 3 that is given). The full rectangle's width below the green rectangle is calculated by adding the known areas and dividing by (14/3).
56/(14/3) is equivalent to 56*(3/14) which is 168/14, so 12.
The width of the green rectangle is 12-3=9
The green rectangle's height is 8 - (14/3). 8 - (14/3) = 10/3
Green rectangle's area is 9 * (10/3) = 30 sq units.I've now watched the video. My way was closer to your first method, but I had to do more calculating as
i didn't spot the 3:9 ratio for width.

[devondevon]

30

For area of 7 and 8 , the width = 7/3

For area 8, the length = 8 * 3/7 = 24/7

Hence, the length for area of 7 and 8 = 3 + 24/7 = 45/7

Hence, the length for area of 15 = (15)/45/7= 7/3

Hence, the width for area of 26 is 7/3 + 7/3 = 14/3

Hence, the length for area of 26 is 26* 3/14 = 39/7

Hence, the length of the unknown rectang;e = 39/7 + 24/7 = 63/7 = 9

Hence, the width of the unknow rectangle = 8 - 14/3 = 10/3

Hence, the area of the unknown rectange = 10/3 * 9 = 90/3 =30 answer

[wackojacko]

The ratios of both methods is key to solving. Seeing this perspective and the comparison of two quantities of the same kind is is quite unique. I absolutely love it! 🙂

[ОльгаСоломашенко-ьы]

It was possible to sequentially calculate first the unknown side of the lilac rectangle, then the white one, and so on. Actions with ordinary fractions and that's it.

[alster]

Method 2 is easier and Merry Christmas, PreMath family.

Seasons Greetings from The Philippines 🇵🇭

[wes]

Let h be the height of the yellow rectangle and 3h=14, so h=14/3 and the height of the green rectangle is (24-14)/3=10/3.
Let w*h=w*(14/3)=56, so w=56(3/14)=12. Thus, the green rectangle area is (12–3)(10/3)=30

[cyruschang]

pink rectangle width = 7/3
white rectangle length = 8 ÷ 7/3 = 24/7
blue rectangle width = 15 ÷ (3 + 24/7) = 7/3
yellow rectangle width = 26 ÷ (7/3 + 7/3) = 39/7
green rectangle width = 8 - (7/3 + 7/3) = 12/7
green rectangle length = 24/7 + 39/7 = 63/7 = 9
green rectangle area = 9(12/7) = 108/7

[GaryBricaultLive]

I disagree with the first assumption that the pink square has a height of 1. And the white rectangle is the same.
Given an area = 7 and one dimension = 3, then the height of the pink square is 7/3 and not 1. Then the blue rectangle also has a height 7/3 and not 1. Then the height of the green rectangle is 8 - (2 * 7/3) = 8 - 14/3 = 10/3. The width of the blue rectangle is then 15/(7/3) = 45/7. The width of the yellow square is 26/(14/3) = 39/7 yielding a total width of 45/7 + 39/7 = 84/7 = 12. Therefore the width of the green rectangle = 12 - 3 = 9. And finally the area of the green rectangle is 9 * (10/3) = 30.

[batavuskoga]

I first calculated the width of the rectangle with area 7. Blue rectangle has the same width, because the total area of the pink and white rectangle has the same area
Width is 7/3. Width of yellow rectangle is 14/3, length is 39/7.
Length green rectangle is length white rectangle + length yellow rectangle = 9
Width green rectangle = 8 - width yellow rectangle = 8 - 14/3 = 10/3
Area green rectangle = length * width = 9 * 10/3 = 30

[santiagoarosam]

Rosa =3*(7/3) → Blanco =[8/(7/3)]*(7/3) =(24/7)*(7/3) → Azul =15 =A+(15-A) → 7/A=8/(15-A)→ A=7 =Rosa =3*(7/3) → 15-A =8 =Blanco =(24/7)*(7/3 → → Verde =[(24+39)/7]*[8-(14/3)] =(63/7)*(10/3) =30
Bonito acertijo. Gracias y felices fiestas.

[LuisdeBritoCamacho]

Total Area = 96
Total Height = 8
Total Base = 12
Down Area = 7 + 8 + 15 + 26 = 56
Upper Area = 10 + 30 = 40
Green Area = 30
Why?
7 = 3x <=> x = 7/3
2x = 14/3
8 - 14/3 = 10/3
56 / (14/3) = 12
3 * 10/3 = 10
Green Area = 96 - 56 - 10 = 30

[DB-lgsq]

شكرآ لكم
نضع y هو العرض فيx

نجد y=10/3
x=30

[misterenter-izrz]

Rather clumsy😮, 7/3, 7/3×2=14/3, 26/(14/3)=78/14=39/7, 8/(7/3)=24/7, the width=24/7+39/7=63/7=9, the height =8-14/3=10/3, the area=9×10/3=30 😊.