Question

What is the area of regular hexagon ABCDEF? Explain or show your reasoning.

Answer 1

The calculated area of regular hexagon ABCDEF is 2340 square units

Hwo to determine the area of regular hexagon ABCDEF?

From the question, we have the following parameters that can be used in our computation:

The figure

The area of regular hexagon ABCDEF is calculated as

Area = Area of big rectangle - 4 * Area of small triangles

Using the above as a guide, we have the following:

Area = (26 + 26) * (15 + 15 + 30) - 4 * 1/2 * 26 * 15

Evaluate

Area = 2340

Hence, the area of regular hexagon ABCDEF is 2340 square units

Answer 2

Given: ABCDEF is a regualar hexagon

The regular hexagon can be divided into two congruent trapezoid

The bases of the trapezoid are 60 and 30 and the height of the trapezoid = 26

So, the area of one trapezoid = 0.5 x ( 60 + 30 ) * 26

so, the area of the hexagon = 2 x 0.5 * (60 + 30) * 26 = 2340

Another solution:

The hexagon can be divided into 6 identical triangle

The base of each triangle = 30

The height = 26

so, the area of the hexagon = 6 x 0.5 * 30 * 26 = 2340