Question

Please find the perimeter and the area of the figure below.

Answer 1

Answer:

Total Composite Area: 5/2π in²

Total Composite Perimeter: 3π + 2 in

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Geometry

• Diameter: d = 2r
• Area of a Circle: A = πr²
• Circumference Formula: C = 2πr

Step-by-step explanation:

Step 1: Define

Radius of Circle ABC = 2 in

Radius of Circle AD = 1 in

Step 2: Find Area

Since the formulas are for use for full circles and we only have semicircles, we need to half the formulas.

We add the 2 composite figures to find the total area.

1. [Circle AD] Substitute [AC]:                                                                               A = 1/2π(1 in)²
2. [Circle ABC] Substitute [AC]:                                                                          A = 1/2π(2 in)²
3. [Total] Combine:                                                                                              A = 1/2π(2 in)² + 1/2π(1 in)²
4. Exponents:                                                                                                       A = 1/2π(4 in²) + 1/2π(1 in²)
5. Multiply:                                                                                                           A = 2π in² + 1/2π in²
6. Add:                                                                                                                  A = 5/2π in²

Step 3: Find Perimeter

Since the formulas are for use for full circles and we only have semicircles, we need to half the formulas.

We add the 2 composite figures to find the total perimeter. Don't forget circumference is only the curve of the circle.

1. [Circle AD] Substitute [CF]:                                                                               C = 1/2(2π · 1 in)
2. [Circle ABC] Substitute [CF]:                                                                           C = 1/2(2π · 2 in)
3. [Total] Combine:                                                                                              C = 1/2(2π · 2in) + 1/2(2π · 1 in) + 2 in
4. Multiply:                                                                                                           C = 1/2(4π in) + 1/2(2π in) + 2 in
5. Multiply:                                                                                                           C = 2π in + π in + 2 in
6. Add:                                                                                                                  C = 3π + 2 in

Answer 2

Hello!

Area:

$\large\boxed{\frac{5}{2}\pi in^{2}}$

Perimeter:

$\large\boxed{3\pi + 2 inch}$

We can divide the figure into two semicircles:

One semicircle of radius 2 inch (Arc ABC) and another semicircle of radius 1 inch (Arc AD)

Find the area using the formula for the area of a semicircle:

A = 1/2(πr²)

Find the area for each semicircle:

Arc ABC:

A = 1/2π(2²)

A = 1/2(4π)

A = 2π

Find the area of semicircle AD:

A = 1/2π(1²)

A = 1/2π(1)

A = 1/2π

Add the two areas together:

1/2π + 2π = 5/2π inches squared.

Perimeter:

Use the formula for the circumference of a semicircle:

C = 1/2(2rπ)

Use the equation to solve for the perimeter of each semicircle.

Semicircle ABC:

C = 1/2(2(2)(π))

C = 2π inch

Semicircle AD:

C = 1/2(2(1)(π))

C = 1π inch

There is also a 2 inch segment that must be incorporated, so the total perimeter is:

2π + 1π + 2 = 3π + 2 inches.