Question

In the given figure, AP $\parallel$ BQ $\parallel$ CR. What will be ar($△$AQC)?

• A. ar($△$ABQ)
• B. ar($△$CQR)
• C. ar($△$PQA)
• D. ar($△$PBR)

Answer 1

The correct option is D ar($△$PBR)

Since △ABQ and △PBQ lie on the same base BQ and are between the same parallels AP and BQ,

∴ Area (△ABQ) = Area (△PBQ) ... (1)

Again, △BCQ and △BRQ lie on the same base BQ and are between the same parallels BQ and CR.

∴ Area (△BCQ) = Area (△BRQ) ... (2)

On adding equations (1) and (2), we obtain

Area (△ABQ) + Area (△BCQ) = Area (△PBQ) + Area (△BRQ)

⇒ Area (△AQC) = Area (△PBR)