Figure 1 shows a sketch of a design for a scraper blade - Edexcel - A-Level Maths Pure - Question 7 - 2015 - Paper 2

To find the perimeter of AOBCDA, we consider each side:

• AB = 16 cm
• DC = 7 cm
• OA = OB = 8 cm (radius of the circles)

Thus:

$$\text{Perimeter} = AB + DC + OA + OB = 16 + 7 + 8 + 8 = 39 ext{ cm}$$

To 3 significant figures, the perimeter is 39.0 cm.

To find the area of AOBCDA, we need the area of triangle COD and the two circular sectors OBC and ODA:

1. Area of Triangle COD: Using the formula:

$$\text{Area}_{triangle} = \frac{1}{2} \times b \times h$$

Where base = CD = 7 cm and height can be calculated using

$$\text{Area}_{triangle} = \frac{1}{2} \times 7 \times 8 \times \sin(0.906) \\ \approx 25.2 ext{ cm}^2$$

2. Area of the sectors OBC and ODA: The angle for each sector is 0.906 radians, so the area for each sector is:

$$\text{Area}_{sector} = \frac{r^2}{2} \times \theta = \frac{8^2}{2} \times 0.906 \\ = 28.8 ext{ cm}^2$$

Total area of two sectors:

$$$$

3. Total Area AOBCDA:

$$\text{Total Area} = \text{Area}_{triangle} + \text{Area}_{sectors} \approx 25.2 + 57.6 = 82.8 ext{ cm}^2$$

Final area to 3 significant figures is 82.8 cm².