6/10/20155.5: Special Right Triangles 5.5: Special Right Triangles and Areas of Regular Polygons...
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Transcript of 6/10/20155.5: Special Right Triangles 5.5: Special Right Triangles and Areas of Regular Polygons...
![Page 1: 6/10/20155.5: Special Right Triangles 5.5: Special Right Triangles and Areas of Regular Polygons Expectations: G1.2.4 : Prove and use the relationships.](https://reader036.fdocuments.in/reader036/viewer/2022071706/56649d365503460f94a0efe1/html5/thumbnails/1.jpg)
04/18/23 5.5: Special Right Triangles
5.5: Special Right Triangles and Areas of Regular
PolygonsExpectations:
G1.2.4: Prove and use the relationships among the side lengths and the angles of 30º- 60º- 90º
triangles and 45º- 45º- 90º triangles.
G1.5.1: Know and use subdivision or circumscription methods to find areas of polygons
G1.5.2: Know, justify and use formulas for the perimeter and area of a regular n- gon.
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ACT Prep
If one diagonal of a rhombus is 12 inches long and the other is 32 inches long, how many inches long, to the nearest hundredth of an inch, is a side of the rhombus?
A.8.54
B.17.09
C.34.17
D.35.78
E.48.00
04/18/23 5.5: Special Right Triangles
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04/18/23 5.5: Special Right Triangles
If a square has area of x2 square units, what is the length of one of its diagonals?
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04/18/23 5.5: Special Right Triangles
45-45-90 Right Triangle Theorem
If a leg of a 45-45-90 right triangle is x units long, then the hypotenuse is x√2 units long.
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04/18/23 5.5: Special Right Triangles
30-60-90 Right Triangles
a. sketch an equilateral triangle with sides of 2x units long.b. draw an altitude of the triangle.c. label all known measures.d. what is the length of the altitude?
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04/18/23 5.5: Special Right Triangles
30-60-90 Right Triangle Theorem
In a 30-60-90 right triangle, if the length of the shorter leg is x units, then the longer leg is x√3units and the hypotenuse is 2x units long.
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04/18/23 5.5: Special Right Triangles
The hypotenuse of a 30-60-90 right triangle is 20 cm. What are the lengths of the other 2 sides?
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What is the perimeter of a 30-60-90 right triangle if the length of the hypotenuse is 8 mm?
04/18/23 5.5: Special Right Triangles
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ACT Prep
If the length of a diagonal of a square is 18 inches long, what is the area of the square, in square inches?
A. 9√2
B. 36√2
C. 72
D. 162
E. 324
04/18/23 5.5: Special Right Triangles
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ACT Prep
If the length of each side of a regular hexagon is 10 centimeters long, what is the area of the hexagon, to the nearest centimeter?
A.25√3
B.60
C.100√3
D.150√3
E.600√3
04/18/23 5.5: Special Right Triangles
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04/18/23 5.5: Special Right Triangles
Center of a Regular Polygon
The center of a regular polygon is the point which is equidistant from the vertices of the regular polygon.
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04/18/23 5.5: Special Right Triangles
Apothem of a regular polygon
An apothem of a regular polygon is a segment with one endpoint at the center of the regular polygon and the other endpoint on the polygon, such that the segment is perpendicular to a side of the polygon.
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04/18/23 5.5: Special Right Triangles
Center and apothem of a regular polygon
Center of the regular octagon
Apothem of the regular octagon
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04/18/23 5.5: Special Right Triangles
Area of a Regular Polygon
1. Locate the center of the regular polygon.
2. Triangulate the polygon using the center as a common vertex.
3. What type of triangles are formed?
4. Draw the altitudes of the triangles.
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04/18/23 5.5: Special Right Triangles
Area of a Regular Polygon
5.What are the altitudes in terms of the polygon?
6. What is the area of one triangle?
7. What is the area of the regular polygon expressed as a product?
8. Change to using the perimeter.
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04/18/23 5.5: Special Right Triangles
Area of a Regular Polygon Theorem
If a regular polygon has area of A square units, perimeter of p units and an apothem of a units, then
A =
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04/18/23 5.5: Special Right Triangles
Assignment
pages 336-338, numbers 10-17(all), 22-38(evens), 44, 45