Question

In the given figure, how many
triangles are there?​

Answer 1

Answer:

16

Step-by-step explanation:

Answer 2

We can first divide this diagram into 2 parts – Part A and Part B and find the no. of triangles in each case.

Part A:

Please refer attachment for diagrammatical representation.

This figure has 8 triangles:

Δ1, Δ2, Δ3 and Δ4 ----- (4)

Δ1 and Δ2 form a single triangle ----- (1)

Δ3 and Δ4 form a single triangle ----- (1)

Δ2 and Δ3 form a single triangle ----- (1)

Δ4 and Δ1 form a single triangle ----- (1)

So, total no. of triangles in Part A = 4 + 1 + 1 + 1 + 1 = 8 triangles

Part B

Please refer attachment for diagrammatical representation.

This figure has 14 triangles.

There are two main triangles. ----- (2)

Part 4, 5 and 1 form a single triangle ----- (1)

Part 3, 6 and 2 form a single triangle. ----- (1)

Δ8 and Δ7 are two different triangles. ----- (2)

Δ8 and Δ7 form a single triangle. ----- (1)

Δ4 and Δ3 are two different triangles. ----- (2)

Δ1 and Δ2 are two different triangles. ----- (2)

Δ1 and Δ2 form a single triangle. ----- (1)

Part 8 and 5 form a single triangle. ----- (1)

Part 7 and 6 form a single triangle. ----- (1)

So, total no. of triangles in Part B = 2 + 1 + 1 + 2 + 1 + 2 + 2 + 1 + 1 + 1 = 14 triangles.

Therefore total no. of triangles in the figure = Part A + Part B

= 8 + 14 = 22 triangles.