The diagram shows a circle and an equilateral triangle - Edexcel - GCSE Maths - Question 14 - 2018 - Paper 2

Since one side of the equilateral triangle is the diameter of the circle, the length of one side is:

$s = 2r = 2 \times 7.0 = 14.0 \text{ cm}$

For an equilateral triangle, the height $h$ can be calculated using:

$h = \frac{\sqrt{3}}{2} s$

Substituting the value of $s$:

$h = \frac{\sqrt{3}}{2} \times 14.0 \approx 12.12 \text{ cm (to 2 decimal places)}$

The area $A$ of an equilateral triangle is given by:

$A = \frac{1}{2} \times b \times h$

where $b$ is the base and $h$ is the height. In this case, the base $b = 14.0$ cm:

$A = \frac{1}{2} \times 14.0 \times 12.12 \approx 84.84 \text{ cm}^2$

Rounding to 3 significant figures, the area of the triangle is:

$A \approx 84.8 \text{ cm}^2$