10.7: Chapter 10 Review
Difficulty Level: At Grade
Created by: CK12
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Keywords, Theorems and Formulas
 Perimeter
 The distance around a shape. Or, the sum of all the edges of a twodimensional 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*}
A=bh .
 Perimeter of a Rectangle

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

\begin{align*}A= \frac{1}{2} bh\end{align*}
A=12bh or \begin{align*}A=\frac{bh}{2}\end{align*}A=bh2
 Area of a Trapezoid

The area of a trapezoid with height \begin{align*}h\end{align*}
h and bases \begin{align*}b_1\end{align*}b1 and \begin{align*}b_2\end{align*}b2 is \begin{align*}A=\frac{1}{2} h(b_1+b_2)\end{align*}A=12h(b1+b2) .
 Area of a Rhombus

If the diagonals of a rhombus are \begin{align*}d_1\end{align*}
d1 and \begin{align*}d_2\end{align*}d2 , then the area is \begin{align*}A=\frac{1}{2} d_1 d_2\end{align*}A=12d1d2 .
 Area of a Kite

If the diagonals of a kite are \begin{align*}d_1\end{align*}
d1 and \begin{align*}d_2\end{align*}d2 , then the area is \begin{align*}A=\frac{1}{2} d_1 d_2\end{align*}A=12d1d2 .
 Area of Similar Polygons Theorem

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

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

If \begin{align*}d\end{align*}
d is the diameter or \begin{align*}r\end{align*}r is the radius of a circle, then \begin{align*}C=\pi d\end{align*}C=πd or \begin{align*}C=2 \pi r\end{align*}C=2πr .
 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*}
ABˆ=mABˆ360∘⋅πd or \begin{align*}\frac{m \widehat{AB}}{360^\circ} \cdot 2 \pi r\end{align*}mABˆ360∘⋅2πr
 Area of a Circle

If \begin{align*}r\end{align*}
r is the radius of a circle, then \begin{align*}A=\pi r^2\end{align*}A=πr2 .
 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*}
r is the radius and \begin{align*}\widehat{AB}\end{align*}ABˆ is the arc bounding a sector, then \begin{align*}A= \frac{m\widehat{AB}}{360^\circ} \cdot \pi r^2\end{align*}A=mABˆ360∘⋅πr2 .
 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*}
s and there are \begin{align*}n\end{align*}n sides in a regular polygon, then the perimeter is \begin{align*}P=ns\end{align*}P=ns .
 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*}
n sides with length \begin{align*}s\end{align*}s in a regular polygon and \begin{align*}a\end{align*}a is the apothem, then \begin{align*}A=\frac{1}{2} asn\end{align*}A=12asn or \begin{align*}A=\frac{1}{2} aP\end{align*}A=12aP , 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 CK12 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:
Aug 15, 2016
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