Question 3 of 14intermediate💡 UnderstandShort Answer2 marks

What measurements would you need to find the area of a regular hexagon?

Correct Answer

To find the area of a regular hexagon, we need:

(1) Side length and apothem: Area = ½ × perimeter × apothem = ½ × (6 × side) × apothem

(2) Side length alone: Area = (33\sqrt{3}/2) × side²

(3) Divide into 6 equilateral triangles: Area of each triangle = (3\sqrt{3}/4) × side² Total area = 6 × (3\sqrt{3}/4) × side² = (33\sqrt{3}/2) × side²

Exercise: Figure it Out (Section 3) | Q: 3 | (Page Page 13)
For More Understanding

Explanation

The chapter explains that any polygon can be divided into triangles. A regular hexagon can be divided into 6 equilateral triangles by joining the center to each vertex. Each equilateral triangle has area = (3\sqrt{3}/4) × side², so total area = 6 × (3\sqrt{3}/4) × side² = (33\sqrt{3}/2) × side².

Solution Steps

  1. Step 1: A regular hexagon can be divided into 6 equilateral triangles.

  2. Step 2: Need the side length of the hexagon.

  3. Step 3: Area of each equilateral triangle = (3\sqrt{3}/4) × side².

  4. Step 4: Total area = 6 × (3\sqrt{3}/4) × side² = (33\sqrt{3}/2) × side².

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