Answer:
The area of the figure is (100 + 50π) cm²
The area of the figure is 257.1 cm² to the nearest tenth
Step-by-step explanation:
The figure is consists of a square with side length 10 cm, and four semi-circles the diameter of each one is equal to the side length of the square
Area of the figure = area of square + 4 × area of a semi-circle
- Area of a square = s², where s is the length of its side
- Area of semi-circle = [tex]\frac{1}{2}[/tex] πr², where r is the radius of it
∵ The length of the side of the square is 10 cm
∴ s = 10 cm
∵ Area of the square = s²
∴ Area of the square = (10)² = 100
∴ Area of the square is 100 cm²
∵ The diameter of the circle is equal to the side of the square
∴ The diameter of the circle = 10 cm
∵ The radius of a circle is half the diameter of the circle
∴ The radius of the semi-circle = [tex]\frac{1}{2}[/tex] × 10 = 5
∴ The radius of the semi-circle = 5 cm
Now lets find the area of a semi-circle
∵ Area of semi-circle = [tex]\frac{1}{2}[/tex] πr²
∴ Area of semi-circle = [tex]\frac{1}{2}[/tex] π(5)² = 12.5π
∴ Area of each semi-circle is 12.5π cm²
Lets find the area of the figure
∵ Area figure = Area of square + 4 × area of a semi-circle
∴ Area figure = 100 + 4 × 12.5π
∴ Area figure = 100 + 50π
∴ The area of the figure is (100 + 50π) cm²
Substitute π by its value in the calculator
∴ Area figure = 100 + 50(3.141592654)
∴ Area figure = 257.0796327
- Round it to the nearest tenth
∴ The area of the figure is 257.1 cm²
