Question

MNOPQR is a hexagon of side 6 cm each. Find the area of the given hexagon.

Answer 1

Answer:

Step-by-step explanation:

Side of hexagon (a) = 6 cm

Area of hexagon= 3 underoot3× a²/2

= 3 underoot3 × 6cm / 2

= 93.53 cm

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Answer 2

Given:

MNOPQR is a hexagon of side length 6cm.

To Find:

The area of the given hexagon is?

Solution:

The given problem can be solved using the concepts of equilateral triangles.

1. The side length of the hexagon is 6cm.

2. A regular hexagon is a combination of 6 equilateral triangles. The 6 equilateral triangles have the same side length.

3. Hence, the side length of each equilateral triangle is 6cm.

4. Consider an equilateral triangle of side length s units. The area of the triangle is given by the formula,

=> Area of the triangle = (0.5)x(base)x(height)

=> Base of the triangle is s units,

=> The height of the triangle can be calculated by Pythagoras theorem,

=> (Hypotenuse)² = (base/2)² + (height)², ( Divide the equilateral triangle into two halves ).

=> s² = (s/2)² + (height)²,

=> s² - s²/4 = (height)²,

=> 3s²/4 = (height)²,

=> height = √(3)* (s/2) units.

5. Therefore, the area of an equilateral triangle is,

=> Area of the equilateral triangle = (0.5)*(s)*√(3)* (s/2),

=> Area of the equilateral triangle = √(3)*(s²/4) units.

=> Area of the equilateral triangle = √(3)*(36/4),

=> Area of the equilateral triangle = 9√(3) cm².

6. The area of the hexagon is 6x(area of the equilateral triangle),

=> Area of the hexagon = 6 x 9√(3),

=> Area of the hexagon = 54√(3),

=> Area of the hexagon = 93.53 cm².

Therefore, the area of the hexagon is 93.53 cm².