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 will calculate the lengths of the triangle edges and the arc lengths:

1. The length of AB is given as 16 cm.
2. Lengths of sides OA and OB are both 8 cm (as they are radii of the circle).
3. The length of DC is given as 7 cm.

Putting it all together for the perimeter:

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

Thus, the perimeter of AOBCDA is 39.0 cm, correct to 3 significant figures.

To find the area, we will calculate the area of the triangle COD and the areas of the sectors OBC and ODA:

1. The area of triangle COD can be found using the formula:

$$ext{Area}_{\triangle} = \frac{1}{2} \cdot b \cdot h$$

Here, if the height is calculated using sine:

$$\text{Area} = \frac{1}{2} \cdot 8 \cdot 7 \cdot \sin(0.906) \approx \frac{1}{2} \cdot 8 \cdot 7 \cdot 0.789 \approx 28.0 ext{ cm}^2$$

2. The area of each sector is given by:

$$ext{Area}_{sector} = \frac{1}{2} \cdot r^2 \cdot \theta = \frac{1}{2} \cdot 8^2 \cdot 0.906 ext{ (for one sector)} \\= 28.928 ext{ cm}^2$$

Thus, for two sectors:

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3. Adding the area of the triangle:

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