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

To determine the area of the flag, we need to find the area of triangle XYZ and then add it to the area of the sector ZYW.

First, for the area of triangle XYZ:

The base XY = 7 cm, and the height (YW) = 5 cm.

Using the formula:

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

Now, we add the area of the triangle to the area of the sector:

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

Rounding to 2 decimal places gives us:

$A_{flag} = 26.25 \text{ cm}^2$

To calculate the perimeter XYWZ, we need the lengths of XY, YW, and ZY, plus the arc length ZW.

1. Lengths given: XY = 7 cm, YW = 5 cm.

2. To find ZY:

   • Using the sine rule in triangle YXZ given that angles sum up to 180 degrees, we first find angle XYZ.

3. For arc ZW, we use the formula for arc length:

$L = r \times \theta$ where:

• $r = 5 cm$ and $\theta = 0.7 rad$.

So,

$L = 5 \times 0.7 = 3.5 \text{ cm}$

Finally, the perimeter is:

$P = XY + YW + ZY + L = 7 + 5 + ZY + 3.5$

Finding ZY using known angles, assuming ZY = x, we determine:

$P = 15.5 + x$

Calculating and rounding gives the final perimeter to 2 decimal places as:

$P = 26.79 \text{ cm}$