Answer:
The diameter of the semi-circle is 5 units
A = 9.82 units²
Step-by-step explanation:
In a circle the inscribed angle subtended by an arc of measure 180° (semi-circle) is a right angle
That means the angle whose vertex lies on a semi circle is a right angle
∵ Arc BC is a semi-circle
∵ Δ ABC is a right triangle
- That means BC is the diameter of the semi-circle and angle A
is the right angle because A lies on the arc BC
∵ In Δ ABC
∵ m∠A = 90°
∵ AB = 3 units
∵ AC = 4 units
- Use Pythagoras theorem to find the length of BC
∵ (BC)² = (AB)² + (AC)²
∴ (BC)² = (3)² + (4)²
∴ (BC)² = 9 + 16
∴ (BC)² = 25
- Take √ for both sides
∴ BC = 5 units
∵ BC is the diameter of the semi-circle
∴ The diameter of the semi-circle is 5 units
∵ Area of the circle = πr²
- Multiply it by half to find the area of the semi-circle
∴ Area of semi-circle = [tex]\frac{1}{2}[/tex] πr²
∵ The length of the radius is half the length of the diameter
of the circle
∴ r = [tex]\frac{1}{2}[/tex] (5) = 2.5 units
∴ A = [tex]\frac{1}{2}[/tex] π (2.5)²
∴ A = 9.817477042
- Round it to the nearest hundredth
∴ A = 9.82 units²
