### Perimeter of Composite Figures with Circular Arcs**Task:** Find the perimeter for the following figures. All arcs shown are arcs of circles. Either leave the answer in terms of $ \pi $ by entering answers with the word pi, or use 3.14 for pi and round your answer to the nearest 10th.#### Figure 15This figure is composed of a rectangle and two semicircular arcs on the shorter sides. The inner dimensions of the rectangle are given as follows:- The length of the rectangle is 8 units.- The radius of the semicircle is 2 units.To find the perimeter of the figure:1. Calculate the circumference of the full circle and then take half of it for each semicircle.2. Add the length of the two straight sides of the rectangle.- The circumference of a full circle is $ 2\pi r $.- For a semicircle, the length is $ \pi r $.Here, $ r = 2 $:- Perimeter of each semicircle = $ 2 \pi \times 2 \div 2 = 2\pi $ units.Two semicircles together form a full circle:- Perimeter of the arcs combined = $ 2\pi \times 2 = 4\pi $ units.Next, the combined length of the straight sides:- Total straight length = $ 8 $ (top of the rectangle) + $ 8 $ (bottom of the rectangle) = 16 units.Thus, the total perimeter:\[ \text{Perimeter} = 16 + 4\pi \text{ units} \]#### Figure 16This figure is composed of a rectangle with four quarter circles removed from the corners. The dimensions of the rectangle are provided:- The length is 16 units.- The height is 10 units.To find the perimeter:1. Calculate the perimeter of the full rectangle.2. Subtract the lengths of the straight cuts from the quarters of circles and add the arc lengths.For the rectangle:- Perimeter without cuts = $ 2 \times (16 + 10) = 52 $ units.Each quarter circle removed has a radius of 3 units (since the difference in horizontal side indicates 3 as the parts cut off).- Circumference of full circles for both short and long sides = \( 2\pi \

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Description: ### Perimeter of Composite Figures with Circular Arcs**Task:** Find the perimeter for the following figures. All arcs shown are arcs of circles. Either leave the answer in terms of $ \pi $ by entering answers with the word pi, or use 3.14 for pi a

15) There are 2 semi circles and one rectangle in the given figure. So, from the given figure…

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Find the perimeter for the following figures. All arcs shown are the arcs of circles. Either leave in terms of T by entering answers with the word pi, or use 3.14 for pi and round your answer to the nearest 10th. 16 15. 16. 10 10

Find the perimeter for the following figures. All arcs shown are the arcs of circles. Either leave in terms of T by entering answers with the word pi, or use 3.14 for pi and round your answer to the nearest 10th. 16 15. 16. 10 10

PREALGEBRA

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ISBN:9781938168994

Author:OpenStax

Publisher:OpenStax

Chapter9: Math Models And Geometry

Section9.3: Use Properties Of Angles, Triangles, And The Pythagorean Theorem

Problem 108E: On a map, San Francisco, Las Vegas, and Los Angeles form a triangle whose sides the shown in the...

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Concept explainers

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

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### Perimeter of Composite Figures with Circular Arcs

**Task:** Find the perimeter for the following figures. All arcs shown are arcs of circles. Either leave the answer in terms of $ \pi $ by entering answers with the word pi, or use 3.14 for pi and round your answer to the nearest 10th.

#### Figure 15
This figure is composed of a rectangle and two semicircular arcs on the shorter sides. The inner dimensions of the rectangle are given as follows:
- The length of the rectangle is 8 units.
- The radius of the semicircle is 2 units.

To find the perimeter of the figure:
1. Calculate the circumference of the full circle and then take half of it for each semicircle.
2. Add the length of the two straight sides of the rectangle.

- The circumference of a full circle is $ 2\pi r $.
- For a semicircle, the length is $ \pi r $.

Here, $ r = 2 $:
- Perimeter of each semicircle = $ 2 \pi \times 2 \div 2 = 2\pi $ units.

Two semicircles together form a full circle:
- Perimeter of the arcs combined = $ 2\pi \times 2 = 4\pi $ units.

Next, the combined length of the straight sides:
- Total straight length = $ 8 $ (top of the rectangle) + $ 8 $ (bottom of the rectangle) = 16 units.

Thus, the total perimeter:
\[ \text{Perimeter} = 16 + 4\pi \text{ units} \]

#### Figure 16
This figure is composed of a rectangle with four quarter circles removed from the corners. The dimensions of the rectangle are provided:
- The length is 16 units.
- The height is 10 units.

To find the perimeter:
1. Calculate the perimeter of the full rectangle.
2. Subtract the lengths of the straight cuts from the quarters of circles and add the arc lengths.

For the rectangle:
- Perimeter without cuts = $ 2 \times (16 + 10) = 52 $ units.

Each quarter circle removed has a radius of 3 units (since the difference in horizontal side indicates 3 as the parts cut off).

- Circumference of full circles for both short and long sides = \( 2\pi \

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