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10.6: Chapter 10 Review

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

Triangles and Parallelograms

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

Trapezoids, Rhombi, and Kites

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

Area of Similar Polygons

  • Area of Similar Polygons Theorem

Circumference and Arc Length

  • \begin{align*}\pi\end{align*}π
  • Circumference: \begin{align*}C=\pi d\end{align*}C=πd or \begin{align*}C=2 \pi r\end{align*}C=2πr
  • Arc Length
  • 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 Circles and Sectors

  • Area of a Circle: \begin{align*}A=\pi r^2\end{align*}
  • Sector
  • Area of a Sector: \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 \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.

  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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