how many triangles of any size are there in the star
Answers
Answer:
There are total 20 triangles in the star.
Step-by-step explanation:
Explanation:
First we count the number of triangles made up with unit triangle.
So, the triangle which are made with unit triangles are {1,2,3,4,5,6,7,8,9,10,11,12} .
- Total 12 triangles are there which are mad with unit triangle.
- Now, from the diagram we see that, there are total 6 triangle {(1,8,7,12),(5,9,10,11),(4,8,9,10),(12,11,10,6),(2,8,9,7) and (7,12,3,11)} which are made are made with 4 unit triangle.
- And there are total 2 triangles made up with 9 unit triangles {(1,7,8,12,4,9,10,11,6),(2,3,5,7,8,9,10,11,12)}.
So, the total numbers of triangle are there in the star = 12+ 6 + 2= 20.
Final answer:
Hence, there are total 20 triangles in the given star.
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Answer:
Total number of Triangles in the star = 20
Step-by-step explanation:
Unit triangles = 12
From the given figure we can see there are 12 unit triangles or 12 small triangles.
No triangle can be formed using 2 or 3 unit triangles
Triangles which are formed using 4 units triangles = 6
No triangle can be formed using 5, 6, 7 or 8 unit triangles
Triangles which are formed using 9 units triangles = 2 (The 2 bigger ones)
Total number of triangles formed = 12 + 6 + 2 = 20
Total number of Triangles in the star = 20
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