Honors Geometry B

Unit 5 Lesson 2 Area of Trapezoids, Rhombuses, and Kites   Area of Trapezoid- A=1/2 h(B1+B2)   Area of Rhombus and Kite- Area of rhombus or kite is half the product of the lengths of its diagonals---- A=1/2 D1D2

Unit 5 Lesson 3 Area of Regular Polygons-- Postulate 10-1: If two figures are congruent, then their areas are equal Theorem 10-6: The area of a regular polygon is half the product of the apothem and the perimeter: A=1/2ap

Unit 5 Lesson 4 Perimeters and Areas of Similar Figures-- If it takes eight bags of fertilizers to cover the bean field, about how many bags will be needed to cover the corn field?  Information: Bean field length is 30 meters, Corn field is 40 meters Steps: set up as 30/40 and take out zeroes: 3/4. Then, square the numbers: 9/16 and set up proportion as: 9/16=8/6 and then x should equal 14.2   Theorem 10-7: If the scale factor of two similar figures is a/b then: the ratio of the perimeters is a/b, and the ratio of the perimeters is a^2/b^2

Unit 5 Lesson 5 Trigonometry and Area-- Find area of a regular nonagon with 10-cm sides and 20 degrees at the top of the isosceles triangle Use sin, cos, and tan to find the apothem Use tan 20=5/a. Then: a=5/tan 20. Now, use A=1/2ap and substitute: = 1/2 5/tan 20 times 20 Theorem 10-8-- The area of a triangle is half the product of the lengths of two sides and the sine of the included angle     

Unit 6 Lesson 1 Surface Areas of Prisms and Cylinders-- Prism- a polyhedron with two congruent, parallel faces, called bases. Other faces on the prism are called lateral faces Altitude- perpendicular segment that joins the planes of the bases Height- the length of the altitude    Lateral Area- the sum of the areas of the lateral faces Surface Area- sum of the lateral area and the area of the two bases Lateral Area of any right prism= ph Surface Area of any right prism= LA+2B Cylinder- a solid that has two congruent bases that are circles. The altitude of a cylinder is a perpendicular segment that joins the planes of the bases     Lateral Area of Cylinder= 2PIr*h Surface Area of Cylinder= LA+2B    or     2PIrH+2PIr^2

Unit 6 Lesson 3 Surface Areas of Pyramids and Cones-- Lateral Area of Pyramid-- the sum of the areas of the congruent lateral faces             Formula: 1/2sl    or    1/2 base*height times 4 Surface Area of Pyramid-- the lateral area plus area of base   Lateral Area of Cone= pi*r*l Surface Area of Cone= LA+ pi*r^2

Unit 6 Lesson 4 Volumes of Prisms and Cylinders-- volume of a cube is e^3 or edge Cavalieri's Principle- if two space figures have the same height and cross sectional area at every level, then they have the same volume Volume of a Prism= Area of the base* height   Volume of a Cylinder= pi*r^2*h

Unit 6 Lesson 5 Volumes of Pyramids and Cones-- Volume of a Pyramid- 1/3*Area of Base* Height Volume of a Cone- 1/3* Area of Base* Height

Unit 6 Lesson 6 Surface Areas and Volumes of Spheres-- SA- 4PI*r^2 Volume of a Sphere- 4/3PI*r^3

Unit 6 Lesson 7 Areas and Volumes of Similar Solids-- Theorem 11-12: If the scale factor of two similar solids is a:b then, 1. the ratio of their corresponding areas is a^2:b^2      2. and the ratio of their corresponding volumes is a^3:B^3   If you are finding the scale factor of two similar figures that has the volumes listed, then put the given volumes in fraction form and take the cube root.  If you are finding the scale factor of two similar figures that has the areas listed, then put the given areas in fraction form and take the square root.