How many triangles and squares are there in the following figure ?

Options

A. 24 triangles, 5 squares
B. 28 triangles, 4 squares
C. 24 triangles, 4 squares
D. 28 triangles, 5 squares

Answer

D

Explanation

In the given figure, label all the points of intersection as follows:

There are in all 28 triangles in the given fig. namely AIB, AIE, BIF, EIF, BJC, BJE, CJG, FJG, CKD, CKG, DKH, GKH, ABE, ABF, AEF, BEF, BCF, BCG, BFG CFG, CDG, CDH, CGH, DGH, AFC, EBG, FCH, BGD, and there are in all 5 squares in the given fig namely ABFE, BCGF, CDHG, IBJE, JCKG.