Figure 2 shows a flag XYWZ - Edexcel - A-Level Maths Pure - Question 6 - 2018 - Paper 4

The area of the flag consists of the area of the sector ZYW and the area of triangle XYZ.

1. Area of Triangle XYZ:

   Using the formula for the area of a triangle:

   $A = \frac{1}{2} \times base \times height$

   Here, we can consider XY as the base (7 cm) and use the height as the radius of the sector (5 cm):

   $A_{XYZ} = \frac{1}{2} \times 7 \times 5 = 17.5 \text{ cm}^2$

2. Total Area of the Flag:

   Now, combining both areas:

   $\text{Total Area} = A_{sector} + A_{triangle} = 8.75 + 17.5 = 26.25 \text{ cm}^2$

So, rounding to 2 decimal places, the area of the flag is 26.25 cm².

To find the perimeter of the flag XYWZ, we need to sum the lengths of all sides:

1. From the point Y to X: 7 cm (given).

2. From Y to W: 5 cm (given).

3. Length ZW can be found using Pythagoras’ Theorem. Since ZY is the opposite side of angle ZYW:

   Using the sine function:

   \approx 3.22 \text{ cm} $$

4. Length XZ can be calculated using the cosine function:

   \approx 7 \times 0.764 \approx 5.35 \text{ cm} $$

Now, adding these lengths together: