WeCP Figure Counting Quiz 1

The squares are AFOE, FBGO, GOHC, OEDH, PJOI, KJLO, LMNO, ONQI, ABCD, KPQM.

Thus there are 10 squares in total.

The squares are AMLE, MBHL, HCJL, LJDE, EFLK, FMLG, GHIL, LIJK, ABCD, AEJH.

Each box contains 6 triangles, so four box contains 24 triangles.

If we sum up all the triangles, this sums up to 44 triangles.

Side of the larger square has 6 small squares .

On counting,

the total number of blue squares = 18

Therefore, factorial of 18x18 = 324

There are 16 squares as marked.

 

Then: (1 && 2&& 6 && 4) , (2 && 3 && 7 && 6), (3 && 4 && 7 && 8) ,

(5 && 6 && 10 && 9), (6 && 7 && 10 && 11), (7 && 8 && 11 && 12),

(9 && 10 && 13 && 14), (10 && 11 && 15 && 14), (11 && 12 && 15 && 16),

 

Then: (1 && 2 && 3 && 5 && 6 && 7 && 9 && 10 && 11),

(2 && 3 && 4 && 6 && 7 && 8 && 10 && 11 && 12),

(5 && 6 && 7 && 9 && 10 && 11 && 13 && 14 && 15),

(6 && 7 && 8 && 10 && 11 && 12 && 14 && 15 && 16),

 

And one big square taking all the small squares.

 

Thus, 16+9+4+1 = 30.

Small triangles = (AEF, AEG, GDH, CFH), (IEK, IFL, JLH, JKG), (IOK, IOL, JOL, KOJ)

Big triangles = IKL, JKL, IJK, IJL Thus, total triangles = 16 =>

Ans – (2)

Total number of smallest squares of unit (1x1) = 10

Total number of squares of unit (2x2) = 5

Total number of squares of unit (3x3) = 2

Total number of squares of unit (4x4) = 1

 

Thus, total squares = 10+5+2+1 = 18.

Here we can observe carefully that there are four squares (AEOH, EBFO, HOGD, OFGC).

In each square, there are a total of 6 triangles. So total triangles in these squares are 6x4 = 24.

 

Inside square PQRS, there are 8 triangles (PQO, QRO, RSO, SOP, PQR, QRS, RSP, SPQ).

 

In the larger square ABCD, again there are 8 larger triangles.

 

Hence, total number of triangles = 24+8+8 = 40

In each square (AEOH & OFCG), there are a total of 4 triangles. So total triangles in these squares are 4x2 = 8.

 

In each square (EBFO, HOGD & PQRS), there are a total of 6 triangles. So total triangles in these squares are 6x3 = 18.

 

In the larger square ABCD, again there are 2 larger triangles.

 

Hence, total number of triangles = 8+18+2 = 28

 

Total number of smallest squares = 10

Side of the larger square has 6 small squares .

The larger square is composed of 6x6 smaller squares.

 

Generalizing the given condition,

Total number of squares in the given figure is given by

Total = \Sigma (side^2) = \Sigma(6^2)

= \frac{n(n+1)(2n+1)}{6}

= \frac{6(6+1)(2\times 6+1)}{6}

= \frac{6\times 7\times 13}{6}

= 91

In each square (AEOH & OFCG), there are a total of 16 triangles. So total triangles in these squares are 16x2 = 32.

 

In each square (EBFO & HOGD), there are a total of 6 triangles. So total triangles in these squares are 6x2 = 12.

 

Inside square PQRS, there are 8 triangles (PQO, QRO, RSO, SOP, PQR, QRS, RSP, SPQ).

 

In the larger square ABCD, again there are 8 larger triangles.

 

Hence, total number of triangles = 32+12+8+8 = 60