The area of each of the 16 square regions in the figure abov

Question

Untitled.png The area of each of the 16 square regions in the figure above is T. What is the area of the shaded region? A. \frac{13T}{3} B. 5T C. \frac{16T}{3} D. \frac{11T}{2} E. 7T Please provide detailed explanations!

Bunuel · Accepted Answer

The whole area = 16T. The areas of three unshaded triangles are = T + 6T + 4T = 11T (half of a rectangle with area of 2 + half of a rectangle with area of 12 + half of a rectangle with area of 8). The area of the shaded region = 16T - 11T = 5T. Answer: B. Similar question to practice: what-is-the-area-of-a-triangle-with-the-following-vertices-125983.html

fozzzy · Answer

So basically what you have done is count the squares and calculated the area's I have modified the image and added color ( Red,Black and blue) so

Black has 4*2*1/2
Red has 4*3*1/2
Blue has 2*1*1/2

is this correct and then subtract from the total?

Bunuel · Answer

Yes, that's correct.

madn800 · Answer

16T- \frac{1}{2} *2 \sqrt{T} * \sqrt{T} )+( \frac{1}{2} *4 \sqrt{T} *3 \sqrt{T} )+( \frac{1}{2} *2 \sqrt{T} *4 \sqrt{T} )] = 5T

satsymbol · Answer

Bunuel.. can you please elaborate on "The areas of three unshaded triangles are = T + 6T + 4T = 11T (half of a rectangle with area of 2 + half of a rectangle with area of 12 + half of a rectangle with area of 8)."
I not able to follow this part.

AKG1593 · Answer

Option B.
Let T be any convenient no. say 36.
Side of each smaller square=6
Side of bigger square=6*4=24
Area shaded=24^2-(area of 3 unshaded right triangles)
=576-36-144-216
=180
Which is 5*36
Ans:5T

Posted from my mobile device

Bunuel · Answer

Untitled.png The areas of three unshaded triangles are = Half of the area of blue rectangle with area of 2T , thus T; Half of the area of black rectangle with area of 8T , thus 4T. Half of the area of red rectangle with area of 12T , thus 6T. T + 4T + 6T = 11T. Hope it's clear.

750300 · Answer

my answer is
The 2nd horizontal line divides the shape into two triangles having the same base and the same ht.

area=2*1/2* sqrt(T)*(1+1+.5)*(sqrt(T)(1+1)
 =5T

Is my approach correct??

T1101 · Answer

Rather simple, but maybe more time consuming approach is to simply estimate and count the fraction of the shaded areas in each square:

\frac{1}{3}+\frac{2}{3}+\frac{1}{3}+\frac{1}{3}+\frac{2}{3}+\frac{2}{3}+\frac{3}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{15}{3}=5

CEdward · Answer

Maybe I am just missing the point of these questions? It's quite easy to see that the shaded pieces fit together to give you 5T.

Am I missing something?

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The area of each of the 16 square regions in the figure abov

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