Question

How many triangles will be there when the pattern is extended to have 32 polygons?

• A. 18
• B. 10
• C. 14
• D. 16

Answer 1

The correct option is D 16

Solution:
Say:
Let’s find out the rule of the pattern to find the number of triangles when the pattern is extended to 32 polygons.
Step:

• 2 triangles are followed by 2 trapezoids in the given pattern.
• So, the rule of the pattern is 2 triangles followed by 2 trapezoids.
• Let’s extend the pattern till 32 polygons as shown on the whiteboard.
• According to the rule, a set of 4 shapes comprises half triangles and half trapezoids.
• So, a set of 32 polygons (8 times 4 = 32) will comprise of half triangles and half triangles and half trapezoids.
• Therefore, in a set of 32 polygons, there will be 16 triangles and 16 trapezoids.
• We can verify this by counting from the whiteboard.
• Hence, Option C is correct.