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Identify the number of base segments (n).

Chemistry

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Answer

45\text{45}

Step-by-step solution

3 steps

  1. Identify the number of base segments (nn).

    The lines originating from the apex divide the base into 5 smaller segments.
    So, n=5n=5.

  2. Identify the number of horizontal levels (mm).

    There are 3 distinct horizontal lines that form bases for triangles (the bottom line, the middle line, and the top line).
    So, m=3m=3.

  3. Calculate the total number of triangles.

    The formula for the number of triangles in such a figure is given by:

    Number of triangles=n(n+1)2×m\text{Number of triangles} = \frac{n(n+1)}{2} \times m

    Substitute the values of n=5n=5 and m=3m=3:

    Number of triangles=5(5+1)2×3\text{Number of triangles} = \frac{5(5+1)}{2} \times 3 Number of triangles=5×62×3\text{Number of triangles} = \frac{5 \times 6}{2} \times 3 Number of triangles=302×3\text{Number of triangles} = \frac{30}{2} \times 3 Number of triangles=15×3\text{Number of triangles} = 15 \times 3 Number of triangles=45\text{Number of triangles} = 45

    The total number of triangles in the figure is 45\text{45}.

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