Mathematics, 27.12.2020 23:40 ashleymspears

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

Answers: 3

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Answer from: jillian0013

Total Composite Area: 5/2π in²

Total Composite Perimeter: 3π + 2 in

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

to Right

Geometry

Diameter: d = 2rArea of a Circle: A = πr²Circumference 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.

[Circle AD] Substitute [AC]: A = 1/2π(1 in)²[Circle ABC] Substitute [AC]: A = 1/2π(2 in)²[Total] Combine: A = 1/2π(2 in)² + 1/2π(1 in)²Exponents: A = 1/2π(4 in²) + 1/2π(1 in²)Multiply: A = 2π in² + 1/2π in²Add: 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.

[Circle AD] Substitute [CF]: C = 1/2(2π · 1 in)[Circle ABC] Substitute [CF]: C = 1/2(2π · 2 in)[Total] Combine: C = 1/2(2π · 2in) + 1/2(2π · 1 in) + 2 inMultiply: C = 1/2(4π in) + 1/2(2π in) + 2 inMultiply: C = 2π in + π in + 2 inAdd: C = 3π + 2 in

Answer from: Jxsolvez

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.

Answer from: Quest

Hey bby was a good way i just got

Answer from: Quest

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.

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