The diagram shows a circle and an equilateral triangle - Edexcel - GCSE Maths - Question 13 - 2018 - Paper 2

The side of the equilateral triangle is the diameter of the circle. Therefore,

$\text{Diameter} = 2r = 2 \times 7 = 14 \, \text{cm}$

The area A of an equilateral triangle with side length a is given by:

$A = \frac{\sqrt{3}}{4} a^2$

Substituting in the side length we found:

$A = \frac{\sqrt{3}}{4} (14)^2$

Calculating:

$A = \frac{\sqrt{3}}{4} \times 196 = 49\sqrt{3}$

Using (\sqrt{3} \approx 1.732), we find:

$A \approx 49 \times 1.732 \approx 84.8 \, \text{cm}^2$

Thus, rounding this value to 3 significant figures gives an area of:

$A \approx 84.9 \, \text{cm}^2$