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10.7: Chapter 10 Review

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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) A=bh.
Perimeter of a Rectangle
P=2b+2h, where b is the base (or width) and h is the height (or length).
Perimeter of a Square
P=4s
Area of a Square
A=s^2
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
A=bh.
Area of a Triangle
A= \frac{1}{2} bh or A=\frac{bh}{2}
Area of a Trapezoid
The area of a trapezoid with height h and bases b_1 and b_2 is A=\frac{1}{2} h(b_1+b_2).
Area of a Rhombus
If the diagonals of a rhombus are d_1 and d_2, then the area is A=\frac{1}{2} d_1 d_2.
Area of a Kite
If the diagonals of a kite are d_1 and d_2, then the area is A=\frac{1}{2} d_1 d_2.
Area of Similar Polygons Theorem
If the scale factor of the sides of two similar polygons is \frac{m}{n}, then the ratio of the areas would be \left( \frac{m}{n} \right)^2.
\pi
The ratio of the circumference of a circle to its diameter.
Circumference
If d is the diameter or r is the radius of a circle, then C=\pi d or C=2 \pi r.
Arc Length
The length of an arc or a portion of a circle’s circumference.
Arc Length Formula
length of \widehat{AB}=\frac{m \widehat{AB}}{360^\circ} \cdot \pi d or \frac{m \widehat{AB}}{360^\circ} \cdot 2 \pi r
Area of a Circle
If r is the radius of a circle, then A=\pi r^2.
Sector of a Circle
The area bounded by two radii and the arc between the endpoints of the radii.
Area of a Sector
If r is the radius and \widehat{AB} is the arc bounding a sector, then A= \frac{m\widehat{AB}}{360^\circ} \cdot \pi r^2.
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 s and there are n sides in a regular polygon, then the perimeter is 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 n sides with length s in a regular polygon and a is the apothem, then A=\frac{1}{2} asn or A=\frac{1}{2} aP, where P is the perimeter.

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. regular pentagon
  5. parallelogram
  6. regular dodecagon

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 \frac{4}{3}. If the area of the larger rectangle is 96 \ units^2, 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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