Geometry
Chapter 11: Measuring Length and Area
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Assignment
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Topic
11.1 Areas of Triangles and Parallelograms
How can we find the area of a polygon?
The area of a square is the square of the length of its side.
If two polygons are congruent, then they have the same area.
The area of a region is the sum of the areas of its nonoverlapping parts.
The area of a rectangle is the product of its base and height, 𝐴 = 𝑏ℎ.
The area of a parallelogram is the product of a base and its corresponding height, 𝐴 = 𝑏ℎ.
11.1
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p.726 48-54
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11.2
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p.736 44-48
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11.3
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p.743 35-41
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11.4
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p.752 42-48
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11.5
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The area of a triangle is one half the product of a base and its corresponding height, 𝐴 = 2 𝑏ℎ.
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11.2 Areas of Trapezoids, Rhombuses, and Kites
How are the areas of trapezoids and rectangles related? How are the areas of rhombuses and kites related?
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The area of a trapezoid is one half the product of the height and the sum of the lengths of the bases, 𝐴 = 2 ℎ (𝑏1 + 𝑏2 ).
1
The area of a rhombus is one half the product of the lengths of its diagonals, 𝐴 = 2 𝑑1 𝑑2 .
1
2
The area of a kite is one half the product of the lengths of its diagonals, 𝐴 = 𝑑1 𝑑2 .
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11.3 Perimeter and Area of Similar Figures
If we know the area of a polygon, how can we use the side length of a similar polygon to find its area?
If two polygons are similar with the lengths of corresponding sides in the ratio of 𝑎: 𝑏, then the ratio of their areas
𝑆𝑖𝑑𝑒 𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑃𝑜𝑙𝑦𝑔𝑜𝑛 𝐼
𝑎
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑃𝑜𝑙𝑦𝑔𝑜𝑛 𝐼
𝑎2
is 𝑎2 : 𝑏 2 . That is, If 𝑆𝑖𝑑𝑒 𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑃𝑜𝑙𝑦𝑔𝑜𝑛 𝐼𝐼 = 𝑏 , then 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑃𝑜𝑙𝑦𝑔𝑜𝑛 𝐼𝐼 = 𝑏2 .
4
11.4 Circumference and Arc Length
How can the radius and circumference of a circle used to calculate distance?
Circumference - The distance around a circle.
Arc Length – A portion of the circumference of a circle.
The circumference 𝐶 of a circle is 𝐶 = 𝜋𝑑 or 𝐶 = 2𝜋𝑟, where 𝑑 is the diameter of the circle and 𝑟 is the radius of the
circle.
In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to
360º. That is,
5
̂
𝐴𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝐴𝐵
2𝜋𝑟
=
̂
𝑚𝐴𝐵
,
360º
̂
̂ = 𝑚𝐴𝐵 ∗ 2𝜋𝑟.
or Arc length of 𝐴𝐵
360º
11.5 Areas of Circles and Sectors
How are a circle’s radius, diameter, and area related?
The area of a circle is 𝜋 times the square of the radius, 𝐴 = 𝜋𝑟 2 .
The ratio of the area of a sector of a circle to the area of the whole circle (𝜋𝑟 2 ) is equal to the ratio of the measure of
the intercepted arc to 360º. That is,
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7
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑠𝑒𝑐𝑡𝑜𝑟 𝐴𝑃𝐵
𝜋𝑟 2
=
̂
𝑚𝐴𝐵
, or
360º
Area of sector 𝐴𝑃𝐵 =
̂
𝑚𝐴𝐵
360º
∗ 2𝜋𝑟 2 .
11.6 Areas of Regular Polygons
How many ways can we find the area of a regular pentagon? What are the advantages of using one method over a
different method?
The center of the polygon and the radius of the polygon are the center and the radius of its circumscribed circle.
The distance from the center to any side of the polygon is called the apothem of the polygon.
A central angle of a regular polygon is an angle formed by two radii drawn to consecutive vertices of the polygon.
The area of a regular n-gon with side length s is one half the product of the apothem 𝑎 and the perimeter P, so
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1
𝐴 = 2 𝑎𝑃, or 𝐴 = 2 𝑎 ∗ 𝑛𝑠.
Chapter 11 Review
Chapter 11 Practice Test
8
Chapter 11 Exam. You have one shot at it so give it your very best effort.
I still have questions about:
p.761 45-51
11.6
Workbook.
1-31 all
Mixed Review
p.768 47-52
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pp. 780 - 783 pp. 282-285
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1-22 all
1-29 all
p. 784 1-17 all
Total Total points /28
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