Mathematics
In the adjoining figure, find:
(i) the number of triangles pointing up.
(ii) the total number of triangles.
Geometrical Concepts
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Answer
The adjoining figure shows a large equilateral triangle whose each side is divided into 3 equal parts, creating a network of 9 unit triangles inside it (6 pointing up and 3 pointing down).
Let us count the triangles of each size carefully.
(i) Triangles pointing up:
- Size 1 (unit upward triangles): There are 6 unit upward triangles.
- Size 2 (formed by 4 unit triangles together): There are 3 such upward triangles.
- Size 3 (the whole large triangle): There is 1 such upward triangle.
Total triangles pointing upwards = 6 + 3 + 1 = 10.
∴ The number of triangles pointing up is 10.
(ii) Triangles pointing down:
- Size 1 (unit downward triangles): There are 3 unit downward triangles.
- No larger downward triangles exist in this figure.
Total downward triangles = 3
Total number of triangles = Triangles pointing up + Triangles pointing down
= 10 + 3 = 13
∴ There are total 13 triangles in the figure.
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