Question

A3. Rohan runs along the boundary of a regular octagonal park. He completes 5 rounds, thus covering a distance of 3600 m. Find the area of the park.​

Answer 1

Given: Rohan covers 5 rounds

Distance covered = 3600m

To Find: Area of the octagonal park

Solution:

Rohan Covers 3600m in 5 rounds.

Therefore, perimeter of the octagonal park = 3600/5  = 720m

Perimeter of Octagon= 8* Length of one side(a)

                        720   = 8 * a                                

                       720/8 = a

                            90 = a

Hence, length of one side of the park is 90m.

Area Of octagon= 2(1+√2)a²

                           = 2(1+ √2) 90*90

                           = 16200(1+√2) m²

(Value of √2 = 1.414)

Area= 16200+ 16200(1.414)

       = 16200+ 22906.8

       = 39106.8 m²

Hence, the area of the octagonal park is 16200(1+√2)m² or 39106.8m².