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18.
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What
is the number of triangles that can be formed whose vertices are the vertices
of an octagon but have only one side common with that of octagon?
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Answer: Option B
Explanation:
When the triangles are drawn in an octagon
with vertices same as those of the octagon and having one side common to that
of the octagon, the figure will appear as shown in (Fig. 1).
Now, we shall first consider the triangles
having only one side AB common with octagon ABCDEFGH and having vertices common
with the octagon (See Fig. 2).Such triangles are ABD, ABE, ABF and ABG i.e. 4
in number.
Similarly, the triangles having only one side
BC common with the octagon and also having vertices common with the octagon are
BCE, BCF, BCG and BCH (as shown in Fig. 3). i.e. There are 4 such triangles.
This way, we have 4 triangles for each side
of the octagon. Thus, there are 8 x 4 = 32 such triangles.
Title :
Analytical Reasoning Q18
Description : 18. What is the number of triangles that can be formed whose vertices are the vertices of an octagon but have only o...
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