Chapter 10 Notes

10-1 Area: Parallelograms Area of a figure is the number of square units it encloses. The stuff inside of a figure. Area of a Parallelogram: product of any base length b and the corresponding height h( always makes a right angle). A = bh

10-1 Area: Parallelograms 6 in 2.5 in A = bh = (2.5)(6) = 15 in 2 4 ft 1 yd A = bh = (4)(3) - change 1 yd to 3 feet = 12 ft 2 or 4 yd 2

10-2 Area: Triangles and Trapezoids Area of a Triangle: A = (bh)/2 or (1/2)bh h b 5 m 2 m 5.4 m 4 ft5 ft 8.2 ft 1.8 ft Find area of triangles below:

10-2 Area: Triangles and Trapezoids-answers Area of a Triangle: A = (bh)/2 or (1/2)bh h b 5 m 2 m 5.4 m 4 ft5 ft 8.2 ft 1.8 ft Find area of triangles below: A= 5 m 2 A= 7.38 ft 2

10-2 Area: Triangles and Trapezoids Area of a Trapezoid: (1/2)h(b 1 + b 2 ) or h(b1 + b2)/2 h b2b2 b1b1 Find the area of the following trapezoids: 7 in 3 in 5 in 4 cm 7 cm 9 cm

10-2 Area: Triangles and Trapezoids-answers Area of a Trapezoid: (1/2)h(b 1 + b 2 ) or h(b 1 + b 2 )/2 h b2b2 b1b1 Find the area of the following trapezoids: 7 in 3 in 5 in 4 cm 7 cm 9 cm A = 15 in 2 A = 22 cm 2

10-2 Area: Triangles and Trapezoids Find the area of the following figures: 10 in 10 ft 5 ft 20 ft 12 in 18 ft 6 in 4in

10-2 Area: Triangles and Trapezoids-answers Find the area of the following figures: 10 in 10 ft 6 ft 20 ft 12 in 18 ft 6 in 4in A = 234 ft 2 A = 108 in 2

10-3 Area: Circles Area of Circle: A = πr 2 r Find Area: 16 m 10 ft 12 mm 6 mm

10-3 Area: Circles - answers Area of Circle: A = πr 2 r Find Area: 16 m 10 ft 12 mm 6 mm A = 201 m 2 A = 21.5 ft 2 A = 339 mm 2

10-4 Space Figures Space Figures: 3-D figures  Prism - two parallel bases that are congruent polygons  Pyramid - has a base that is a polygon. Lateral faces are triangles.  Cylinder - has two parallel bases that are congruent circles  Cone - one circular base and one vertex  Sphere - a 3-d ball

10-4 Space Figures Net - an unfolded space figure

10-4 Space Figures-answers Net - an unfolded space figure Square prism Hexagonal pyramid Pentagonal prism

10-4 Space Figures

10-4 Space Figures-answers Base = rectangle Rectangular prism Base = pentagon Pentagonal pyramid Base = circle cone Base = hexagons Hexagonal prism

10-4 Space Figures

10-4 Space Figures-answers Base = triangles Triangular prism Base = rectangle Rectangular pyramid

10-5 Surface Area: Prisms Lateral area: sum of the area of the faces OR L.A. = ph Surface area: sum of all the faces and bases OR S.A. = ph + 2B p = perimeter of the base B = area of the base h = height

Surface area of a net

Surface area of a net-answers 3300 ft m in 2

SA of Prisms

SA of Prisms-answers 500 in mm 2

10-5 Surface Area of Cylinders Lateral area: product of the circumference of the base and the height OR L.A. = 2πrh Surface area: sum of the lateral area and the areas of the 2 bases OR S.A. = 2πrh + 2πr 2 or 2πr(h +r)

SA of Cylinders

SA of Cylinders-answers cm 2 About 330 cm 2

10-6 Surface Area: Pyramids, Cones, and Spheres Surface Area of a Pyramid: o Lateral Area - area of each triangle added together or the formula: LA = (1/2)Pl or Pl / 2 o Total Surface Area -sum of the area of each triangle and area of the base or the formula: Total SA = (1/2)Pl + B P represents Perimeter of the base of a 3-D figure B represents Area of the base 3-D figure l represents slant height

10-6 Surface Area: Pyramids, Cones, and Spheres Find lateral area and total surface area. Lateral Area: Total Surface Area:

10-6 Surface Area: Pyramids, Cones, and Spheres-answers Find lateral area and total surface area. Lateral Area: Total Surface Area: 80 m = 105 cm 2

10-6 Surface Area: Pyramids, Cones, and Spheres Find lateral area and total surface area. Lateral Area: Total Surface Area:

10-6 Surface Area: Pyramids, Cones, and Spheres-answers Find lateral area and total surface area. Lateral Area: Total Surface Area: 108 cm = 144 cm 2

10-6 Surface Area: Pyramids, Cones, and Spheres Surface Area of a Cone: o Lateral Area - area of the sides LA = πrl o Total Surface Area -sum of the lateral area and area of the base: Total SA = πrl + B or πrl + πr 2

10-6 Surface Area: Pyramids, Cones, and Spheres Lateral Area: Total Surface Area:

10-6 Surface Area: Pyramids, Cones, and Spheres Lateral Area: Total Surface Area: (3.14)(3)(7)= m (3.14)(3 2 ) = 94.2 m 2

10-6 Surface Area: Pyramids, Cones, and Spheres Lateral Area: Total Surface Area:

10-6 Surface Area: Pyramids, Cones, and Spheres-answers Lateral Area: Total Surface Area: (3.14)(7)(15)= ft (3.14)(7 2 ) = ft 2

10-6 Surface Area: Pyramids, Cones, and Spheres Surface Area of a Sphere: Total Surface Area = 4πr 2 SA =

10-6 Surface Area: Pyramids, Cones, and Spheres Surface Area of a Sphere: Total Surface Area = 4πr 2 SA = units squared

10-6 Surface Area: Pyramids, Cones, and Spheres Find surface area of each figure:

10-6 Surface Area: Pyramids, Cones, and Spheres-answers Find surface area of each figure: 216 m m 2

10-7 Volume of Prisms and Cylinders Volume of a prism: product of the area of the base (B) and the height (h) V = Bh OR V = lwh (rectangular prism) V = (bh)H/2 (trianglular prism) H = height of prism Volume of Cylinders: the base area (B) times the height (h) V = Bh OR V = πr 2 h

Answers 628 m cm 3 147,706 in in ft 3 25,434 cm 3

Answers 8139 m ft 3

10-9 Volume: Pyramids, Cones, and Spheres Volume of Cone: V = (1/3) Bh or Bh/3 B = area of the base

10-9 Volume: Pyramids, Cones, and Spheres-answers Volume of Cone: V = (1/3) Bh or Bh/3 B = area of the base 1272 in 3 33 mm 3

10-9 Volume: Pyramids, Cones, and Spheres Volume of a Pyramid: V = (1/3) Bh or Bh/3 B = area of the base

10-9 Volume: Pyramids, Cones, and Spheres-answers Volume of a Pyramid: V = (1/3) Bh or Bh/3 B = area of the base 33 m in 3

10-9 Volume: Pyramids, Cones, and Spheres Volume of a Sphere: V = (4/3) πr 3 or (4πr 3 )/3 B = area of the base

10-9 Volume: Pyramids, Cones, and Spheres-answers Volume of a Sphere: V = (4/3) πr 3 or (4πr 3 )/3 B = area of the base 3052 ft cm 3

10-9b Scaling and Volume Similar solids have the same shape and all their corresponding dimensions are proportional. The ratio of corresponding edge lengths of 2 similar solids is the similarity ratio. Similarity ratio: length of front edge of smaller length of front edge of larger

Each pair of prisms is similar. Find the similarity ratio and ratio of the volumes of each.

Each pair of prisms is similar. Find the similarity ratio and ratio of the volumes of each.-answers Similarity ratio = 1:2 Ratios of volume = 1:8 Similarity ratio = 2:3 Ratios of volume = 8:27

Each pair of prisms is similar. Find the volume of the larger prism.

answers 216 ft yd 3