The diagram shows a regular hexagon made from six equilateral triangles - OCR - GCSE Maths - Question 23 - 2019 - Paper 1

The area of triangle ACB can be calculated using the formula:

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

Here, the base AB = 10 cm and the height BC = 5 cm:

$\text{Area} = \frac{1}{2} \times 10 \times 5 = 25\,\text{cm}^2$

However, since we are dealing with a right triangle, we notice that the height should actually be the vertical height from C to AB.

Given triangle properties and using the formula:

$\text{Area} = \frac{1}{2} \times AC \times BC$

We need to recalculate based on the correct height from C:

Substituting accurately gives:

$\text{Area} = \frac{1}{2} \times 8.66 \times 5 \approx 21.65$

Rounded to 3 significant figures, this gives an area of 21.7 cm².

The area of a regular hexagon can be calculated using the formula:

$\text{Area} = \frac{3\sqrt{3}}{2} s^2$

where s is the length of one side. With s = 10 cm: