find the are and perimeter of each figure showing your process clearly

 

Simple answer:

To find the area and perimeter of the semicircle with a radius of 8 cm, we can use the following formulas:

Area of a Semicircle

The area $𝐴$ of a semicircle is given by:
$𝐴=\frac{1}{2}𝜋{𝑟}^2$Given:

• Radius $𝑟=8$ cm
• $𝜋=3.14$

Substitute the values into the formula:
$𝐴=\frac{1}{2}\times 3.14\times (8{)}^2$
$𝐴=\frac{1}{2}\times 3.14\times 64$
$𝐴=\frac{1}{2}\times 200.96$
$𝐴=100.48{\text{cm}}^2$

Perimeter of a Semicircle

The perimeter $𝑃$ of a semicircle includes the curved part (half the circumference of a full circle) and the diameter. The formula is:
$𝑃=𝜋𝑟+2𝑟$Given:

• Radius $𝑟=8$ cm
• $𝜋=3.14$

Substitute the values into the formula:
$𝑃=3.14\times 8+2\times 8$
$𝑃=25.12+16$
$𝑃=41.12\text{cm}$

Summary

• Area: $100.48{\text{cm}}^2$
• Perimeter: $41.12\text{cm}$

To find the area and perimeter of each semicircle shown in the images, we will use the given dimensions and the value of $𝜋=3.14$.

First Semicircle (Diameter 24 cm)

Radius

The radius $𝑟$ is half of the diameter:
$𝑟=\frac{24}{2}=12\text{cm}$

Area

The area $𝐴$ of a semicircle is given by:
$𝐴=\frac{1}{2}𝜋{𝑟}^2$
Substitute the values:
$𝐴=\frac{1}{2}\times 3.14\times (12{)}^2$
$𝐴=\frac{1}{2}\times 3.14\times 144$
$𝐴=\frac{1}{2}\times 452.16$
$𝐴=226.08{\text{cm}}^2$

Perimeter

The perimeter $𝑃$ of a semicircle includes the curved part (half the circumference of a full circle) and the diameter:
$𝑃=𝜋𝑟+2𝑟$
Substitute the values:
$𝑃=3.14\times 12+24$
$𝑃=37.68+24$
$𝑃=61.68\text{cm}$