# 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) \begin{align*}A=bh\end{align*}.

- Perimeter of a Rectangle
- \begin{align*}P=2b+2h\end{align*}, where \begin{align*}b\end{align*} is the base (or width) and \begin{align*}h\end{align*} is the height (or length).

- Perimeter of a Square
- \begin{align*}P=4s\end{align*}

- Area of a Square
- \begin{align*}A=s^2\end{align*}

- 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
- \begin{align*}A=bh\end{align*}.

- Area of a Triangle
- \begin{align*}A= \frac{1}{2} bh\end{align*} or \begin{align*}A=\frac{bh}{2}\end{align*}

- Area of a Trapezoid
- The area of a trapezoid with height \begin{align*}h\end{align*} and bases \begin{align*}b_1\end{align*} and \begin{align*}b_2\end{align*} is \begin{align*}A=\frac{1}{2} h(b_1+b_2)\end{align*}.

- Area of a Rhombus
- If the diagonals of a rhombus are \begin{align*}d_1\end{align*} and \begin{align*}d_2\end{align*}, then the area is \begin{align*}A=\frac{1}{2} d_1 d_2\end{align*}.

- Area of a Kite
- If the diagonals of a kite are \begin{align*}d_1\end{align*} and \begin{align*}d_2\end{align*}, then the area is \begin{align*}A=\frac{1}{2} d_1 d_2\end{align*}.

- Area of Similar Polygons Theorem
- If the scale factor of the sides of two similar polygons is \begin{align*}\frac{m}{n}\end{align*}, then the ratio of the areas would be \begin{align*}\left( \frac{m}{n} \right)^2\end{align*}.

- \begin{align*}\pi\end{align*}
- The ratio of the circumference of a circle to its diameter.

- Circumference
- If \begin{align*}d\end{align*} is the diameter or \begin{align*}r\end{align*} is the radius of a circle, then \begin{align*}C=\pi d\end{align*} or \begin{align*}C=2 \pi r\end{align*}.

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

- Arc Length Formula
- length of \begin{align*}\widehat{AB}=\frac{m \widehat{AB}}{360^\circ} \cdot \pi d\end{align*} or \begin{align*}\frac{m \widehat{AB}}{360^\circ} \cdot 2 \pi r\end{align*}

- Area of a Circle
- If \begin{align*}r\end{align*} is the radius of a circle, then \begin{align*}A=\pi r^2\end{align*}.

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

- Area of a Sector
- If \begin{align*}r\end{align*} is the radius and \begin{align*}\widehat{AB}\end{align*} is the arc bounding a sector, then \begin{align*}A= \frac{m\widehat{AB}}{360^\circ} \cdot \pi r^2\end{align*}.

- 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 \begin{align*}s\end{align*} and there are \begin{align*}n\end{align*} sides in a regular polygon, then the perimeter is \begin{align*}P=ns\end{align*}.

- 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 \begin{align*}n\end{align*} sides with length \begin{align*}s\end{align*} in a regular polygon and \begin{align*}a\end{align*} is the apothem, then \begin{align*}A=\frac{1}{2} asn\end{align*} or \begin{align*}A=\frac{1}{2} aP\end{align*}, where \begin{align*}P\end{align*} 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 \begin{align*}\frac{4}{3}\end{align*}. If the area of the larger rectangle is \begin{align*}96 \ units^2\end{align*}, 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:

Feb 03, 2016
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