question_answer

Direction: Find the number of triangles in the given figures.

A) 36                    

B) 40  

C) 48                    

D) 50

Correct Answer: C

Solution :

: Let us label the given figure. Triangles made up of one segment each: APQ, AEQ, GBS, BHS, UVW, UWX, UTY, UXY, YJC, YCK, NWD, WDM, UQR, URS, UST and UVQ. Triangles made up of two segments each: UQS, USY, UQW, UWY. Triangles made up of three segments each: AUF, FUB, UBI, UIC, ULC, ULD, UOD and UOA. Triangles made up of four segments each : QYW, SWY, QSW and QSY. Triangles made up of six segments each: UAB, UBC, UDC and UDA. Triangles made up of seven segments each : PSD, QMC, SDK, ANY, BWJ, AGY, EBW and CQH. Triangles made up of twelve segments each : ACD, ABC, BDC and ABD. So, number of total triangles =16+4+8 +4+4+8+4= 48.