Question

9. A quilt pattern will use the block shown in the graph with regular hexagon

Answer 1

From the given coordinates of point A(4, 0), and D (-4, 0), the area of the hexagon is 33.94 units square.

How can the area of the hexagon be found?

The given parameters are;

Shape of the quilt pattern = A regular hexagon

Coordinates of point A = A(4, 0)

Coordinates of point D = D(-4, 0)

Required;

The area of the hexagon

Solution;

The coordinates of the center of the hexagon, P = (0, 0)

A regular hexagon consist of six equilateral triangles.

The length of a side of the triangle = PA

Length of PA = 4 - 0 = 4

Therefore;

Length of a side of the triangle = 4

Height of the triangle = PA × sin(60)

Which gives;

Height of the triangle = 4 × (√3)/2 = 2•√3

Area of one triangle = (4 ÷ 2) × 2•√3 = 4•√2

Area of the 6 triangles is therefore;

A = 6 × 4•√2 = 24•√2

Area of the 6 triangles = Area of the hexagon

Therefore;

• Area of the hexagon = 24•√2 = 33.94 square units.

Learn more about the area of regular shapes here;

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