APPSC Group-I Prelims 2024 Paper II · Question 57

Question 57 of the APPSC Group-I Prelims 2024 Paper II (17 March 2024). Try it first, then open the answer and explanation.

1. Prelims 2024 · P-II · Q57 · Mental Ability & Reasoning · Arithmetic

   If a circle touching all the n sides of a polygon of perimeter 2p has radius r, then the area of the polygon is :

   1. (p + n)/(2r)
   2. (p - n)r
   3. (2p - n)r
   4. pr

   r వ్యాసార్థం గల ఒక వృత్తం 2p చుట్టుకొలత గల బహుభుజి యొక్క అన్ని వైపులు n ని తాకితే, అప్పుడు ఆ బహుభుజి యొక్క వైశాల్యం ఎంత అవుతుంది :

   1. (p + n)/(2r)
   2. (p - n)r
   3. (2p - n)r
   4. pr
   Show answer

   Answer: (4) pr

   సమాధానం: (4) pr

   Joining the centre of the incircle to the vertices splits the polygon into n triangles, each with height r. So Area = (1/2) × r × (sum of all sides) = (1/2) × r × 2p = pr.

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