Answer:
- The shaded area is 66.40 cm²
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The shaded section is the difference of sector OAB and triangle OAC.
Area of sector
Find the measure of angle O
- cos ∠O = OC/OA
- cos ∠O = 5/13
- m∠O = arccos (5/12)
- m∠O = 65.4° (rounded)
Find the area of sector OAB
- A = πr²θ/360
- A = 3.14*13²*65.4/360
- A = 96.40 cm²
Area of triangle
Find the height of triangle
Use Pythagorean
- OA² = OC² + AC²
- 13² = 5² + AC²
- AC² = 169 - 25
- AC² = 144
- AC = √144
- AC = 12
Find area of triangle
- A = bh/2
- A = 5*12/2
- A = 30 cm²
Shaded area
Find shaded area
- A = 96.40 - 30
- A = 66.40 cm²