Question

Someone help please! Having some trouble

Answer 1

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 = $\frac{1}{2}$ 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 = $\frac{1}{2}$ × 10 = 5

∴ The radius of the semi-circle = 5 cm

Now lets find the area of a semi-circle

∵ Area of semi-circle = $\frac{1}{2}$ πr²

∴ Area of semi-circle = $\frac{1}{2}$ 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