Figure 1 is a sketch representing the cross-section of a large tent ABCDEF - Edexcel - A-Level Maths Pure - Question 6 - 2016 - Paper 2

To calculate the area of the sector FBCD, we can use the formula:

$A = \frac{1}{2} r^2 \theta$

Substituting the known values:

• $r = 3.5$ m
• $\theta = 1.77$ radians

The area can then be calculated as follows:

$A = \frac{1}{2} \times (3.5)^2 \times 1.77\ = \frac{1}{2} \times 12.25 \times 1.77 \approx 10.84 \text{ m}^2$

Rounding to 2 decimal places, the area of the sector FBCD is:

10.84 m².

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

1. Area of the triangle AFB:

   The area of triangle AFB can be calculated using:

   $A_{triangle} = \frac{1}{2} \times base \times height$

   Here, the base (AF) is $3.7$ m and the height (BF) is $3.5$ m. Thus, the area is:

   \approx 6.48 ext{ m}^2$$

2. Total Area Computation:

   To find the total area, we add the area of the sector and the area of the triangle:

   $Total\,Area = 10.84 + 6.48 \approx 17.32 m^2$

Rounding this value to 2 decimal places, the total area of the cross-section of the tent is:

17.32 m².