Question

Find the number of triangles in the given figure.

• A. 8
• B. 10
• C. 12
• D. 14

Answer 1

The Correct Option is D

To count the triangles in the figure, systematically break it down:

Identify elementary triangles: Begin by locating and counting the smallest, indivisible triangles. Proceed methodically through the figure.

Identify composite triangles: Form larger triangles by combining two or more elementary triangles. Ensure all unique combinations are accounted for.

Address overlapping triangles: Recognize and count triangles formed by intersecting lines or shared vertices, ensuring each is counted only once.

Verify the count: Review the entire figure to confirm accuracy and eliminate any duplicate counts.

This structured approach, involving dissection and enumeration of combinations, reveals:

• 6 basic triangles.
• 4 triangles formed by combining basic units.
• 4 triangles resulting from intersections and overlaps.

The sum of these components is 14 triangles. Therefore, the figure contains 14 triangles.