Figure 1 is a sketch representing the cross-section of a large tent ABCDEF - Edexcel - A-Level Maths Pure - Question 5 - 2016 - Paper 2

The area of a sector can be calculated using the formula:

$$ext{Area} = \frac{1}{2} r^2 \theta$$

Using the values ( r = 3.5 ) m and ( \theta = 1.77 ) radians:

$$ext{Area} = \frac{1}{2} \times (3.5)^2 \times 1.77 = \frac{1}{2} \times 12.25 \times 1.77 = 10.84\,\text{m}^2$$

Thus, the area of the sector FBCD, rounded to two decimal places, is:

$$\approx 10.84\,\text{m}^2$$

To find the total area of the cross-section, we need to consider both the area of the sector FBCD and the area of triangle BFD.

First, we calculate the area of triangle BFD:

The formula for the area of a triangle is:

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

Using ( ext{base} = BF + FD = 3.5 + 3.5 = 7 ) m and the angle at F:

$$ext{Area}_{\text{triangle BFD}} = \frac{1}{2} \times 7 \times 3.5 \times \sin(1.77)$$

Calculating, we have:

$$\approx \frac{1}{2} \times 7 \times 3.5 \times 0.985 \approx 10.84\,\text{m}^2$$

Now, adding both areas together:

$$\text{Total Area} = 10.84 + 10.84 = 21.68\,\text{m}^2$$

Thus, the total area of the cross-section of the tent, rounded to two decimal places, is:

$$\approx 21.68\,\text{m}^2$$