# 10.7: Chapter 10 Review

Difficulty Level:

**At Grade**Created by: CK-12
**Keywords, Theorems and Formulas**

- Perimeter
- The distance around a shape. Or, the sum of all the edges of a two-dimensional figure.

- Area of a Rectangle
- The area of a rectangle is the product of its base (width) and height (length) .

- Perimeter of a Rectangle
- , where is the base (or width) and is the height (or length).

- Perimeter of a Square

- Area of a Square

- Congruent Areas Postulate
- If two figures are congruent, they have the same area.

- Area Addition Postulate
- If a figure is composed of two or more parts that do not overlap each other, then the area of the figure is the sum of the areas of the parts.

- Area of a Parallelogram
- .

- Area of a Triangle
- or

- Area of a Trapezoid
- The area of a trapezoid with height and bases and is .

- Area of a Rhombus
- If the diagonals of a rhombus are and , then the area is .

- Area of a Kite
- If the diagonals of a kite are and , then the area is .

- Area of Similar Polygons Theorem
- If the scale factor of the sides of two similar polygons is , then the ratio of the areas would be .

- The ratio of the circumference of a circle to its diameter.

- Circumference
- If is the diameter or is the radius of a circle, then or .

- Arc Length
- The length of an arc or a portion of a circle’s circumference.

- Arc Length Formula
- length of or

- Area of a Circle
- If is the radius of a circle, then .

- Sector of a Circle
- The area bounded by two radii and the arc between the endpoints of the radii.

- Area of a Sector
- If is the radius and is the arc bounding a sector, then .

- Segment of a Circle
- The area of a circle that is bounded by a chord and the arc with the same endpoints as the chord.

- Perimeter of a Regular Polygon
- If the length of a side is and there are sides in a regular polygon, then the perimeter is .

- Apothem
- A line segment drawn from the center of a regular polygon to the midpoint of one of its sides.

- Area of a Regular Polygon
- If there are sides with length in a regular polygon and is the apothem, then or , where is the perimeter.

## Review Questions

Find the area and perimeter of the following figures. Round your answers to the nearest hundredth.

- square
- rectangle
- rhombus
- regular pentagon
- parallelogram
- regular dodecagon

Find the area of the following figures. Leave your answers in simplest radical form.

- triangle
- kite
- isosceles trapezoid
- Find the area and circumference of a circle with radius 17.
- Find the area and circumference of a circle with diameter 30.
- Two similar rectangles have a scale factor . If the area of the larger rectangle is , find the area of the smaller rectangle.

Find the area of the following figures. Round your answers to the nearest hundredth.

- find the shaded area (figure is a rhombus)

## Texas Instruments Resources

*In the CK-12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9695.*

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## Date Created:

Feb 22, 2012## Last Modified:

Oct 28, 2015
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