The diagram on the right shows a right-angled triangle with a hypotenuse of length 10 units - Junior Cycle Mathematics - Question 12 - 2017

The hexagon can be divided into 6 equilateral triangles. The area of one equilateral triangle with side length s can be calculated using the formula:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

The height of the triangle can be found as follows:

For an equilateral triangle:

$\text{height} = \frac{\sqrt{3}}{2} s$

Substituting ( s = 10 ):

$\text{height} = \frac{\sqrt{3}}{2} \times 10 = 5\sqrt{3}$

Thus, the area of one triangle is:

$\text{Area} = \frac{1}{2} \times 10 \times 5\sqrt{3} = 25\sqrt{3} \text{ square units}$

Since there are 6 triangles in the hexagon, the total area is:

$\text{Total Area} = 6 \times 25\sqrt{3} = 150\sqrt{3} \text{ square units}$