Answer:
First question: The area of the flower bed is 50.24 feet²
Second question: EF is 13.5 inches
Third question: Area of the figure is 38.47 cm²
Fourth question: The best approximation of the area is 12.56 m² ⇒ 2nd answer
Step-by-step explanation:
First question:
The formula of the area of a circle is A = πr², where r is its radius
∵ A circular flower bed has a radius of 4 feet
∴ r = 4 feet
∵ The area of a circle = πr²
∵ The flower bed is shaped a circle
∴ The area of the flower bed = πr²
∵ π = 3.14
∴ The area of the flower bed = 3.14(4)²
∴ The area of the flower bed = 50.24 feet²
Second question:
Similar triangles have a constant ratio between their corresponding sides
∵ Δ ABC is similar to Δ DEF
∵ The corresponding sides are
AB and DE
BC and EF
AC and DF
∴ [tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]
∵ AB = 5 inches
∵ BC = 9 inches
∵ DE = 7.5 inches
- Use the ratio above to find EF
∵ [tex]\frac{5}{7.5}=\frac{9}{EF}[/tex]
- By using cross multiplication
∴ EF × 5 = 7.5 × 9
∴ 5 EF = 67.5
- Divide both sides by 5
∴ EF = 13.5 inches
Third question:
Area of a quarter circle = [tex]\frac{1}{4}[/tex] × area of the circle
∵ Area of a circle = πr²
∴ Area of a quarter circle = [tex]\frac{1}{4}[/tex] πr²
∵ The figure is a quarter circle with radius of 7 centimeters
∵ π = 3.14
∴ Area of the figure = [tex]\frac{1}{4}[/tex] (3.14)(7)²
∴ Area of the figure = 38.465 cm²
- Round it to the nearest hundredth
∴ Area of the figure = 38.47 cm²
Fourth question:
Area of the circle = πr²
∵ The circle has a diameter 4 meters
- The length of the radius of a circle is half the length of its diameter
∴ The radius of the circle = [tex]\frac{1}{2}[/tex] × 4 = 2 meters
∵ π = 3.14
∴ The area of the circle = 3.14(2)²
∴ The area of the circle = 12.56 meters²
∴ The best approximation of the area is 12.56 m²
