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English and Logical Reasoning Prep Guide
Exam
English and Logical Reasoning Prep Guide
Subject
Logical Reasoning
Chapter
Counting of Figures

English and Logical Reasoning Prep Guide · Logical Reasoning · Counting of Figures

How many triangles are there in the given figure?

How many triangles are there in the given figure? How many triangles are there in the given figure?

Options

  1. A2929
  2. B3838
  3. C4040
  4. D3535

Correct answer

C. 4040

Step-by-step solution

How many triangles are there in the given figure?
The simplest triangles are : Δ PNO; Δ PNM; Δ MPQ; Δ MQR; Δ AQP; Δ AQR; Δ BRA; Δ BRC; Δ SRC; Δ SCD; Δ SGR; Δ SGD; Δ DFG; Δ DFE; Δ TLM; Δ TJK; Δ TLK; Δ TIH; \begin{aligned} & \Delta \text { PNO; } \Delta \text { PNM; } \Delta \text { MPQ; } \\ & \Delta \text { MQR; } \Delta \text { AQP; } \Delta \text { AQR; } \\ & \Delta \text { BRA; } \Delta \text { BRC; } \Delta \text { SRC; } \\ & \Delta \text { SCD; } \Delta \text { SGR; } \Delta \text { SGD; } \\ & \Delta \text { DFG; } \Delta \text { DFE; } \Delta \text { TLM; } \\ & \Delta \text { TJK; } \Delta \text { TLK; } \Delta \text { TIH; }\end{aligned} The triangles composed of two components are: Δ\Delta PON; △\triangle PMA; △\triangle APR; △ RAM; △\triangle RAC; △\triangle RGC; Δ\Delta DGC; Δ\Delta DGE; Δ\Delta MPR; Δ\Delta GRD; △\triangle DCR; △\triangle TMK; Δ\Delta TKI; Δ\Delta TIG The triangles composed of four components are: ΔAMO;△AMC;△CAG;Δ\Delta \mathrm{AMO} ; \triangle \mathrm{AMC} ; \triangle \mathrm{CAG} ;\Delta CGE; Δ\Delta MKI; Δ\Delta GIK; Other triangles are: ΔSPI\Delta \mathrm{SPI}; ΔDQK\Delta \mathrm{DQK} Total number of triangles 18+14+6+2=4018+14+6+2=40
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