How many triangles are there in the given figure?

Correct — B. Take the figure apart before counting anything.

Three outlines overlap: a five-sided figure with its apex at the top, a six-sided figure sharing that apex and the lowest point, and an inner diamond drawn with both of its diagonals.

Rule: count the diamond first, then the thin triangles along each flank.

The diamond with both diagonals gives 4 quarter triangles, plus 4 half triangles — top, bottom, left and right, each made of two quarters. That is 8.

Down the left flank the five-sided outline crosses the six-sided one, and the strip between them breaks into 4 thin triangles.

The right flank mirrors it exactly: another 4.

8 + 4 + 4 = 16 → option (b).

Why the others are wrong

• (a)
  17 — 17 comes from counting a wedge at the very bottom, where the six-sided outline's lowest point looks as though it sits above the base of the five-sided one. The two meet at a single point.
• (c)
  14 — 14 falls two short. The usual omission is a pair of half-diamonds — the whole upper half and the whole lower half, each built from two quarters and easy to overlook once the quarters have been ticked off.
• (d)
  15 — 15 is one short, and the flanks are where a count goes missing. The sliver pinched between an edge of the five-sided outline and a corner of the six-sided one is hard to see at the size this figure prints.

A triangle count is only reliable once the parts have been named. Work out which closed outlines are drawn, then count region by region rather than scanning the whole picture at once.

The single most useful fact here is that a quadrilateral with both diagonals drawn holds 8 triangles, not 4: the four quarters, and then each adjacent pair of quarters forming a larger triangle.

Everything else in this figure is a sliver produced where one outline crosses another.

Key facts

• A quadrilateral with both diagonals drawn contains 8 triangles: 4 quarters and 4 halves.
• The inner diamond here contributes 8 and each flank contributes 4, giving 16.
• Slivers formed where two outlines cross are triangles too, and they are the ones a quick scan drops.

Common traps

• Counting only the 4 quarter triangles inside the diamond and stopping there
• Missing the thin triangles where the five-sided outline crosses the six-sided one
• Reading the lowest point as sitting above the base and adding a phantom wedge

No directly related past PYQ was found.