Figure 1 is a sketch representing the cross-section of a large tent ABCDEF - Edexcel - A-Level Maths Pure - Question 6 - 2017 - Paper 3

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

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

where:

• $A$ is the area of the sector,
• $r = 3.5$ m (the radius), and
• $\theta = 1.77$ radians.

Substituting in the values gives:

$A = \frac{1}{2} \times (3.5)^2 \times 1.77$

Calculating this: $A = \frac{1}{2} \times 12.25 \times 1.77 = 10.84 \text{ m}^2$

Thus, the area of the sector FBCD is approximately 10.84 m².

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

First, we calculate the area of triangle AFB using the formula:

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

Here, the base can be taken as $AF = 3.7$ m and the height (perpendicular distance from point F to line AB) is $3.5$ m:

$A_{triangle} = \frac{1}{2} \times 3.7 \times 3.5 \times \sin(1.77)$

Calculating: $A_{triangle} \approx 6.40 \text{ m}^2$

Finally, summing the areas:

$Total~Area = 10.84 + 6.40 = 17.24 \text{ m}^2$

Thus, the total area of the cross-section of the tent is approximately 17.24 m².