Question

The midpoints of the hexagon are connected to form another hexagon, this pattern continues indefinitely. If the area of the 99th hexagon formed by this pattern is 1, what is the area of the original hexagon?

Answer 1

(4/3)^98units.

Explanation:

By hexagonal property in which cut off the triangles obtained be the joining of m.p of adjacent sides which left 3/4 of total area.

Answer 2

• (4/3)⁹⁸ units²

Explanation:

• Regular hexagons have a property that cutting off the triangles obtained by joining the midpoints of consecutive sides leaves a hexagon of 3/4 of the area.

This means the area of each hexagon inside out starting from the one with unit area is 4/3 of the previous one.

• 99 ⇒ 1
• 98 ⇒ 1*4/3
• 97 ⇒ 1*(4/3)²
• ...
• 1 ⇒ (4/3)⁹⁹⁻¹

The original hexagon has the area of:

• (4/3)⁹⁸ units²