The shape BCD shown in Figure 3 is a design for a logo - Edexcel - A-Level Maths Pure - Question 9 - 2009 - Paper 2

To find the angle ∠DAC, we first recognize that the angle around point A can be calculated using the formula:

$\theta = \frac{2 \pi - \text{α}}{2}$

where α is the angle ∠ BAC (2.2 radians).

Substituting in:

$\theta = \frac{2 \pi - 2.2}{2}$

Calculating:

$\theta \approx \frac{6.283 - 2.2}{2} \approx 2.04 \text{ rad}$ (to 3 significant figures).

The total area of the logo design consists of the area of sector BAC and the areas of triangles BDC and ABD.

1. The area of sector BAC has been calculated as 39.6 cm².
2. For triangles, we can use the following formula:

$A = \frac{1}{2} b h$ For triangle ABD:

• base (AD) = 4 cm
• height (BD) can be derived from the properties of the shape. Suppose we find BD as required.

The area of triangle ABD can be calculated accordingly, and we simplify:

Thus, sum total area will be: $\text{Total Area} = \text{Area sector BAC} + \text{Area triangle ABD} + \text{Area triangle BDC}$ Round the total to the nearest cm² after calculating all areas.