Figure 2 shows a flag XYWZ - Edexcel - A-Level Maths Pure - Question 5 - 2018 - Paper 4

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

First, we find the area of triangle XYZ using the formula:

$A_{triangle} = \frac{1}{2} \times b \times h$

where $b = XY = 7 \, cm$ and the height $h = YW = 5 \, cm$:

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

Now we add the areas:

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

To find the perimeter of the flag, we need to sum the lengths of the sides XY, YZ, ZW, and WX.

We already have:

• $XY = 7 \, cm$
• $YW = 5 \, cm$.

To find $YZ$: Note that in triangle XYZ, we can use the sine rule whereby:

$YZ = YW / \sin(0.7)$

Calculating: $YZ = \frac{5}{\sin(0.7)} \approx 5 / 0.644 = 7.77 \, cm$

For $ZW$, we also use the radius: $ZW = 5 \, cm$

Now summing up: $Perimeter = XY + YZ + ZW + WX = 7 + 7.77 + 5 + 7 = 26.77 \, cm$

To round to 2 decimal places, it becomes 26.79 cm.