Question

Find the difference between the areas of a regular octagon and a regular hexagon if the perimeter of each
is 24cm.
If an equilateral triangle and a regular hexagon have the same perimeter, prove that their areas are in the
5.
mario​

Answer 1

Answer:

Step-by-step explanation:

Given:

Perimeter of regular octagon = 24cm

Perimeter of regular hexagon = 24cm

Difference between the areas =?

Now,

Perimeter of regular octagon = 8 × s

⇒ 24 = 8s

⇒ s = 24/8

⇒ s = 3cm

Area of octagon = 2(1+√2) a²

                           = 2 ( 1 + 1.41) 3² = 2 × 2.41 × 9 ≈ 43.38cm²

Now,

Perimeter of regular hexagon = 6s

⇒ 24 = 6s

⇒ s = 24/6

⇒ s = 4cm

Now, area of regular hexagon = 3√3 s² / 2

                                                   = 3√3 × 4²/2 ≈ 3 × 1.73 × 16/2

                                                   ≈ 5.19 × 8 = 41.52cm²

Now, Difference between the areas = 43.38 - 41.52 ≈ 1.86cm²