+0  
 
+5
4
3102
9
avatar+797 

How many triangles and quadrilaterals are in this diagram?

 Mar 9, 2016

Best Answer 

 #7
avatar+115 
+5

how!?!? lol im just stupid

 Mar 9, 2016
 #1
avatar+115 
0

there are 9 triangles

 Mar 9, 2016
edited by ilovefood  Mar 9, 2016
 #2
avatar+797 
0

9 what

 Mar 9, 2016
 #3
avatar+26 
0

I counted 30 triangles

 Mar 9, 2016
 #4
avatar+797 
0

I have the answers. Tell me when you give up. Then I will tell you the answers.

 Mar 9, 2016
 #5
avatar+115 
0

i give

ilovefood  Mar 9, 2016
 #6
avatar+797 
+5

There are 64 triangles and 36 quadrilaterals.

 Mar 9, 2016
 #7
avatar+115 
+5
Best Answer

how!?!? lol im just stupid

ilovefood  Mar 9, 2016
 #8
avatar+26393 
0

How many triangles and quadrilaterals are in this diagram?

 

 

see: http://www.mathsisfun.com/puzzles/count-the-shapes-solution.html

 

laugh

 Mar 9, 2016
 #9
avatar+26393 
+5

How many triangles and quadrilaterals are in this diagram?

 

 

There is a pattern for the triangles:

if n the number of the lines in the triangle on every side, then the number of triangles is \((n+1)^3\)

 

We have n = 3, so \((n+1)^3 = (3+1)^3 = 4^3 = 64\) triangles.

 

I assume the pattern for the quadrilaterals is:

\(n=0: \quad (0)^2 = 0 \\ n=1: \quad (0+1)^2 =1^2 = 1 \\ n=2: \quad (0+1+2)^2 = 3^2 = 9 \\ n=3: \quad (0+1+2+3)^2 = 6^2 = 36 \\ \dots \\ \text{for n}: \qquad \left[\frac{(n+1)\cdot n}{2} \right]^2 \text{quadrilaterals} \)

We have n = 3, so \( \left[\frac{(n+1)\cdot n}{2} \right]^2 = \left[\frac{(3+1)\cdot 3}{2} \right]^2=\left[\frac{4\cdot 3}{2} \right]^2=6^2=36\) quadrilaterals

 

laugh

heureka  Mar 9, 2016

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