Download Chapter 11 – Areas of Polygons and Circles

Geometry Honors Chapter 11 – Areas of Polygons and Circles
Section 1 – Areas of Parallelograms and Triangles
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 I can use the Pythagorean Theorem to solve for unknown side length of a right triangle.
I can draw right triangles that describe real world problems and label the sides and angles with their given measures.
I can solve right triangles including special right triangles (such as 30-60-90 and 45-45-90) by finding the measures of
all sides and angles in the triangles.
 I can apply geometric methods to solve design problems.
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Area of a Parallelogram – A = bh (which is area = base * height)
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Area of a Triangle – A = ½ bh (which is area = ½ base * height)
1. Find the perimeter and area of parallelogram RSTU
.
2. Find the area of the parallelogram PQRS.
3. SANDBOX. You need to buy enough boards to make the frame of the triangular sandbox shown and
enough sand to fill it. If one board is 3 feet long and one bag of sand fills 9 square feet of the sandbox,
how many boards and bags do you need to buy?
4. The height of a triangle is 7 inches more than its base. The area of the triangle is 60 square inches.
Find the base and height.
Homework – Page 767-768 (11- 33 ODD) and (16, 28, 30, 32, 34,42)
Section 2 – Areas of Trapezoids, Rhombi and Kites
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 I can use the Pythagorean Theorem to solve for unknown side length of a right triangle.
I can draw right triangles that describe real world problems and label the sides and angles with their given measures.
 I can apply geometric methods to solve design problems.
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Area of a Trapezoid – A = ½ h(b1 + b2) (which is area =½ times height times base 1 + base 2)
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Area of a Rhombus or Kite – A = ½ d1*d2 (which means area = ½ times diagonal 1 times diagonal 2)
1. SHAVING: Find the area of steel used to make the razor blade shown below:
2. OPEN ENDED: Miguel designed a deck shaped like the trapezoid shown below. Find the area of the deck.
3. Find the area of each kite or rhombus.
(a)
(b)
4. One diagonal of a rhombus is half as long as the other diagonal. If the area of the rhombus is 64
square inches, what are the lengths of the diagonals?
5. What is the area of the kite shown?
*****Table on Page 776 gives all formulas you need to know!!!!
Homework – Page 777 – 780 (9-21)ODD and (16, 22, 25, 26, 27, 30, 31, 32, 39, 40)
Section 3 – Areas of Circles and Sectors
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 I can define 𝜋 as the ratio of a circle’s circumference to its diameter.
I can use algebra to demonstrate that because 𝜋 is the ratio of a circle’s circumference to its diameter that the
formula for a circle’s circumference must be C = � 𝜋d.
 I can use similarity to derive the formula for the area of a sector.
 I can find the area of a sector.
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Area of a Circle – area = pi times radius squared
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Area of a Sector - area = the section of the arc you want divided by the whole (360) times the area of a circle
1. (a) MANUFACTURING: An outdoor accessories company manufactures circular covers for outdoor
umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in
square inches.
(b) SPORTS: An archery target has a radius of 12 inches. What is the area of the target to the nearest
square inch?
2. (a) ALGEBRA : Find the radius of a circle with an area of 58 square inches.
(b) ALGEBRA: The area of a circle is 196𝜋 square yards. Find the diameter.
3. (a) PIE: A pie has a diameter of 9 inches and is cute into 10 congruent slices. What is the area of one
slice to the nearest hundredth?
(b) CRAFTS: The color wheel is a tool that artists use to organize color schemes. If the diameter of the
wheel is 10 inches and each of the 12 sections is congruent, find the approximate area covered by green
hues.
Homework – Page 785 (9 – 35)ODD and 24, 28, 32, 34, 40, 44, 45)
Secton 4 – Areas of Regular Polygons and Composite Figures
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
 I can use the Pythagorean Theorem to solve for unknown side length of a right triangle.
I can draw right triangles that describe real world problems and label the sides and angles with their given measures.
I can solve right triangles including special right triangles (such as 30-60-90 and 45-45-90) by finding the measures of
all sides and angles in the triangles.
 I can apply geometric methods to solve design problems.
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Center and Radius of a regular polygon – these are the same as the center and a radius of a regular
circle when the polygon is circumscribed within the circle.
 Apothem – a segment drawn form the center of a regular polygon perpendicular to a side of the
polygon. Its length is the height of an isosceles triangle that has 2 radii as legs.
 Central angle of a regular polygon – its vertex is at the center of the polygon and its sides pass
through consecutive vertices of the polygon. The measure of the central angle is 360/#of sides.
1. In the figure, pentagon PQRST is inscribed in circle with center X. Identify the center, a radius, an
apothem, and a central angle of the polygon. Then find the measure of the central angle.
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Area of a regular polygon – only when you are given the base and height!! – A = ½ b*h*# of triangles
A = ½ base*height*# of triangles (or sides in the figure)
2. FURNITURE: The top of the table shown is a regular hexagon with a side length of 3 feet and an
apothem of 1.7 feet. What is the area of the tabletop to the nearest tenth?
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Area of a regular polygon – A = ½ aP (which is Area = ½ * apothem *Perimeter of the polygon)
3. Find the area of each regular polygon. Round to the nearest tenth.
(a) regular hexagon
(b) regular pentagon
Day 1 Homework – Page 795-798 (8-13, 26, 35)
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Composite Figure – a figure that can be separated into different parts such as triangles, squares,
rectangles, etc. You find the area of each part and then add or subtract the extra parts that are needed.
4. POOL: The dimensions of an irregularly shaped pool are shown. What is the area of the surface of the
pool?
Guided Practice Example 4:
4A.
4B.
5. Find the area of the shaded figure.
Guided Practice Example 5
5A.
5B.
DO #26 – 28 in class*
Day 2 Homework – Page 796-797 (14-20, 22, 23, 24, 27, 28, 29, 30, 31)
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Section 5 – Areas of Similar Figures
I can use geometric shapes, their measures and their properties to describe objects.
If 2 polygons are similar (~), then their areas are proportional to the square of the scale factor between
them.
Example: If ABCD ~ FGHJ, then area of FGHJ = FG
area of ABCD AB
1. If ABCD ~ PQRS and the area of ABCD is 48 inches, find the area of PQRS.
2. The area of triangle ABC is 98 square inches. The area of triangle RTS is 50 square inches. If triangle
ABC ~ triangle RTS, find the scale factor from triangle ABC to triangle RTS and the value of x.
3. CRAFTS: The area of one side of a skyscraper is 90,000 square feet. The area of the corresponding
side of a scale model is 200 square inches. If the skyscraper is 720 feet tall about how tall is the model?
Homework – Page 805 (6-13) ALL