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# 10.6: Chapter 10 Review

Difficulty Level: At Grade Created by: CK-12

## Keywords, Theorems and Formulas

Triangles and Parallelograms

• Perimeter
• Area of a Rectangle: A=bh\begin{align*}A=bh\end{align*}
• Perimeter of a Rectangle P=2b+2h\begin{align*}P=2b+2h\end{align*}
• Perimeter of a Square: P=4s\begin{align*}P=4s\end{align*}
• Area of a Square: A=s2\begin{align*}A=s^2\end{align*}
• Congruent Areas Postulate
• Area Addition Postulate
• Area of a Parallelogram: A=bh\begin{align*}A=bh\end{align*}
• Area of a Triangle: A=12 bh\begin{align*}A=\frac{1}{2} \ bh\end{align*} or A=bh2\begin{align*}A=\frac{bh}{2}\end{align*}

Trapezoids, Rhombi, and Kites

• Area of a Trapezoid: A=12h(b1+b2)\begin{align*}A=\frac{1}{2} h(b_1+b_2)\end{align*}
• Area of a Rhombus: A=12d1d2\begin{align*}A=\frac{1}{2} d_1 d_2\end{align*}
• Area of a Kite: A=12d1d2\begin{align*}A=\frac{1}{2} d_1 d_2\end{align*}

Area of Similar Polygons

• Area of Similar Polygons Theorem

Circumference and Arc Length

• π\begin{align*}\pi\end{align*}
• Circumference: C=πd\begin{align*}C=\pi d\end{align*} or C=2πr\begin{align*}C=2 \pi r\end{align*}
• Arc Length
• Arc Length Formula: length of ABˆ=mABˆ360πd\begin{align*}\widehat{AB} = \frac{m \widehat{AB}}{360^\circ} \cdot \pi d\end{align*} or mABˆ3602πr\begin{align*}\frac{m \widehat{AB}}{360^\circ} \cdot 2 \pi r\end{align*}

Area of Circles and Sectors

• Area of a Circle: A=πr2\begin{align*}A=\pi r^2\end{align*}
• Sector
• Area of a Sector: A=mABˆ360πr2\begin{align*}A=\frac{m \widehat{AB}}{360^\circ} \cdot \pi r^2\end{align*}
• Segment of a Circle

## Review Questions

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

1. square
2. rectangle
3. rhombus
4. equilateral triangle
5. parallelogram
6. kite

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

1. triangle
2. kite
3. isosceles trapezoid
4. Find the area and circumference of a circle with radius 17.
5. Find the area and circumference of a circle with diameter 30.
6. Two similar rectangles have a scale factor 43\begin{align*}\frac{4}{3}\end{align*}. If the area of the larger rectangle is 96 units2\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.

1. 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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Feb 22, 2012
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CK.MAT.ENG.SE.1.Geometry-Basic.10.6