Figure 1 is a sketch representing the cross-section of a large tent ABCDEF - Edexcel - A-Level Maths Pure - Question 5 - 2017 - Paper 3

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

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

Substituting the known values:

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

we have:

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

Calculating this:

1. First, calculate $(3.5)^2 = 12.25$,
2. Then, $\frac{1}{2} \times 12.25 \times 1.77 = 10.84$ m².

Thus, the area of 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 to the area of triangle FBD.

The area of triangle FBD is given by:

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

Where:

• base = BF = 3.5 m,
• height = AF = 3.7 m.

Substituting into the formula:

$A_{triangle} = \frac{1}{2} \times 3.5 \times 3.7 = 6.475$ m².

Now, adding the areas together:

$Total Area = Area_{sector} + Area_{triangle} = 10.84 + 6.475 = 17.315$ m².

Rounding to two decimal places, the total area is:

17.32 m²