Question

Calculate the area of a regular hendecagon with a side length of 4 meters.

A 149.85 m²
③ 44 m²
©
125.46 m

Answer 1

1288m2

Explanation:

A= 1/2aP

Where: a is apothem; perpendicular distance from the center of polygon to one of the sides

and p is the perimeter

When you drop the perpendicular distance, it will bisect the side into two, which the form number of triangles.

4m/2=2m and form the right angle

Using the angle rule: SOHCATOA

Angle side:360/11=32.72

One side length=4tan32.72

14.64m then multiplying by 2=29.27, hence the perimeter is given by

29.72x11=322

A=1/2x4x322

A=1288m2

Answer 2

Answer:option A is the correct answer.

Explanation:

A hendecagon is a polygon with eleven sides. Therefore, a regular hendecagon has 11 equal sides and eleven equal angles.

The formula for determining the area of a hendecagon is expressed as

Area = 11/4 × Cot(π/11) × s^2

Where

s represents the side length of the hendecagon.

From the given information,

s = 4 meters

2π = 360 degrees

π = 360/2 = 180 degrees.

Therefore,

Area = 11/4 × Cot(180/11) × 4^2

Area = 11/4 × Cot(16.363636) × 4^2

Area = 11/4 × 3.4057 × 16

Area = 149.85m^2