How many triangles are there in the given figure?

The correct answer is 11.

To systematically count all the triangles in the given geometric figure, let us label the key outer vertices and inner intersection points as follows:
- A: Top-left corner vertex
- B: Top-right corner vertex
- C: Middle-left vertex
- D: Bottom-most apex vertex
- E: Middle-right vertex
- P: Inner intersection point of line segment AD and line segment BC
- Q: Inner intersection point of horizontal line segment PQ and line segment BD

Step 1: Count single elementary triangles (triangles consisting of only 1 simple region)
1. Triangle APB (top region bounded by vertices A, P, and B)
2. Triangle APC (upper-left region bounded by vertices A, P, and C)
3. Triangle BPQ (upper interior region bounded by vertices B, P, and Q)
4. Triangle CPD (lower-left region bounded by vertices C, P, and D)
5. Triangle PQD (lower-center region bounded by vertices P, Q, and D)
6. Triangle BED (outer right region bounded by vertices B, E, and D)
Number of single elementary triangles = 6.

Step 2: Count composite triangles formed by combining 2 adjacent simple regions
7. Triangle ABC (formed by combining Triangle APB and Triangle APC)
8. Triangle ACD (formed by combining Triangle APC and Triangle CPD)
9. Triangle BPD (formed by combining Triangle BPQ and Triangle PQD)
Number of 2-region composite triangles = 3.

Step 3: Count composite triangles formed by combining 3 adjacent simple regions
10. Triangle ABD (formed by combining Triangle APB, Triangle BPQ, and Triangle PQD)
11. Triangle BCD (formed by combining Triangle CPD, Triangle PQD, and Triangle BPQ)
Number of 3-region composite triangles = 2.

Step 4: Calculate the total number of triangles

$\text{Total Triangles}=6+3+2=11$

Thus, there are a total of 11 triangles in the given figure.