b = base h = height Area is the number of square units that make up the inside of the shape is a square with a side length of 1 of any unit

Transcription

1 Area is the number of square units that make up the inside of the shape of 1 of any unit is a square with a side length Jan 29-7:58 AM b = base h = height Jan 29-8:31 AM 1

2 Example 6 in Jan 29-8:33 AM A rectangle is a special type of parallelogram height (h) base (b) Jan 29-8:38 AM 2

3 Example 10 ft 20 ft Jan 29-8:45 AM b h Each triangle represents half of the rectangle If we know that the formula for the area of a know that the area of a triangle is half that Jan 29-8:50 AM 3

4 1 2 bh area base height Jan 29-8:56 AM Example 8 ft 17 ft 15 ft Jan 29-8:58 AM 4

5 Practice ft 10.5 ft Jan 29-8:35 AM cm 35.2 cm 5 cm 15 cm Jan 29-8:45 AM 5

6 3. 1 / 7 cm 35 / 42 cm 2 Jan 29-8:47 AM in 8.6 in Jan 29-8:59 AM 6

7 5. 15 cm 12cm 17.4 cm 9 cm 12.6 cm Jan 29-9:04 AM 6. The 6th grade art students are making a mosaic using tiles in the shape of right triangles. Each tile has leg measures of 3 cm and 5 cm. If there are 200 tiles in the mosaic, what is the area of the mosaic? Jan 29-9:04 AM 7

8 1) Break the figure up into rectangles and triangles 2) Find the area of each figure 3) Add all of the areas together Jan 29-9:05 AM Example 12 ft 1 13 ft 12 ft 13 ft 2 5 ft 12 ft 5 ft Jan 29-9:06 AM 8

9 Practice 1. 8 m 1 2 m 2 4 m Jan 29-9:10 AM in 6.5 in 12 in Jan 29-9:11 AM 9

10 Area of Compound Figures In order to find the area of compound figures (think of compound words) you may need to find the measurement of missing sides. Jan 29-9:15 AM Example 1. A B F E units, and DE = 7 units, find the lengths of DC and BC. D C Jan 29-9:23 AM 10

11 2. A B Using the same figure...if DC = 10 units, F E units, and BC = 54 units, find the D C lengths of AB and DE. Jan 29-9:24 AM 1) Break the figure up into rectangles and triangles 2) Find the area of each figure 3) Add all of the areas together Jan 29-9:24 AM 11

12 Example 2 m 2 m 1 4 m 2 9 m 3 7 m Jan 29-9:29 AM Practice 1. 8 ft 12 ft 25 ft Jan 29-9:30 AM 12

13 2. 29 m 7 m 12 m 19 m Jan 29-9:32 AM km 7 km 24 km 25 km 25 km 24 km 35 km Jan 29-9:33 AM 13

14 4. Hal's backyard has a patio, a walkway, and garden. What percent of the total area of Hal's backyard is the area taken up by the patio, walkway, and garden? Round to the nearest whole percent. 6 ft 5 ft Patio Lawn Walkway Lawn Garden 3 ft 8 ft 9 ft Jan 29-9:34 AM 5. Find the area of the deck around the pool. Pool 50 m Deck 90 m 15 m 25 m Jan 29-9:37 AM 14

15 is the amount of space inside a 3-D figure. It is measured in cubic units, and the volume is the number of cubic units needed to fill the inside of the figure. Jan 29-9:42 AM Each layer in the rectangular prism has = 12 cubes Since there are layers in the rectangular prism, there are 12 =. Each of the 24 cubes has a volume of 1 cm 3. So, the volume of the rectangular is 24 1 cm 3 =. Jan 29-9:42 AM 15

16 One layer in the rectangular prism has 5 5 = 25 cubes Since there are 5 layers in the rectangular prism, there are 25 = 125. Each of the 125 cubes has a volume of 1 cm 3. So, the volume of the rectangular is cm 3 =125. Jan 29-10:16 AM volume length width height Jan 29-10:18 AM 16

17 Example Jan 29-10:24 AM Practice 1. A toy company is packaging its toys to be shipped. Some of the very small toys are placed inside a cube shaped box with side lengths of 1 / 2 in. These smaller boxes are then placed into a shipping box with dimensions of 10 in X 4 in X 6 in. How many small toys can be packed into the larger box for shipping? 6 in 10 in 4 in Jan 29-10:41 AM 17

18 What is the volume of one toy box? Use the number of toys that can be shipped in the box to determine the volume of the box. Jan 29-10:48 AM 2. Calculate the volume of the rectangular prism. 4 1 / 2 m 1 1 / 2 m 3/ 4 m Jan 29-10:54 AM 18

19 3. What is the volume of this prism? 4 2 / 3 in 9 in 1 1 / 3 in Jan 29-10:54 AM Linda fills the rectangular prism with cubes that have side lengths of 1 / 3 in. How many cubes does she need to fill the rectangular prism? Jan 29-10:56 AM 19

20 4. 4.5cm 2.75 cm 24 cm Jan 29-11:27 AM 5. The base of a rectangular prism has an area of 3 1 / 4 in 2 height of the prism is 2 1 / 2 in. Determine the volume of the rectangular prism. Jan 29-11:28 AM 20

21 6. The area of the base of a sandbox is 9 1 / 2 ft 2. The volume of the sandbox is 7 1 / 8 ft 3. Determine the height of the sandbox. Jan 29-11:29 AM 7. Determine the volume of the water that would need to fill the rest of the tank. 1/ 2 m 3/ 4 m 1 / 2 m 1 1 / 4 m Jan 29-11:29 AM 21

22 8. 12 m 3 m 9 1 / 2 m 2m 2 m Jan 29-11:30 AM Nets are two dimensional figures that can be folded to create a three dimensional solid. The shapes in the net become the faces of the three dimensional figure. Jan 29-1:05 PM 22

23 Nets can be used to find the surface area of three dimensional figures. Surface area is the area of all the faces of a three dimensional figure. Jan 29-1:20 PM 1) find the area of each face 2) add the areas together figure: Jan 29-1:21 PM 23

24 Cube Faces: Edges: Vertices: Jan 29-1:05 PM Sketch: Surface Area: Jan 29-1:11 PM 24

25 Rectangular Prism Faces: Edges: Vertices: Jan 29-1:07 PM Sketch: Surface Area: Jan 29-1:12 PM 25

26 Triangular Prism Faces: Edges: Vertices: Jan 29-1:13 PM Sketch: Surface Area: Jan 29-1:13 PM 26

27 Square Pyramid Faces: Edges: Vertices: Jan 29-1:13 PM Sketch: Surface Area: Jan 29-1:13 PM 27

28 prism is a solid geometric figure whose two bases are parallel identical polygons and whose sides are parallelograms. pyramid is a solid geometric figure formed by connecting a polygonal base and a point forming triangular lateral faces. Jan 29-1:15 PM Practice 1. Break this rectangular prism down into its net. Include measurements Jan 29-1:17 PM 28

29 2. A juice box measures 4 inches high, 3 inches long, and 2 inches wide. Draw a net to represent all faces of the juice box, and be sure to include the measurements. Then calculate the surface area of the juice box. Jan 29-1:17 PM 3. Calculate the surface area of the rectangular prism below. 8 cm 6 cm 15 cm Jan 29-1:19 PM 29

30 4. Calculate the surface area of the rectangular prism below Jan 29-1:23 PM 5. Calculate the surface area of the rectangular prism below. 7.9 m 32.3 m 24.7 m Jan 29-1:24 PM 30

31 6. Cinema Theaters created a new popcorn box in the shape of a rectangular prism. The new popcorn box has a length of 6 inches, a width of 3.5 inches, and a height of 3.5 inches, but does not include a lid. a) How much popcorn does the box hold? Jan 29-1:24 PM b) How much material is needed to create the box? Jan 29-1:25 PM 31

32 Polygons on the Coordinate Plane coordinate plane: 1) Look for the coordinates that are 2) Find the absolute value of each coordinate 3) -If the signs are the same: subtract the absolute values -If the signs are different: add the absolute values Jan 29-1:26 PM Practice 1. Plot and connect the points A(3,2), B(3,7), and C(8,2). Name the shape and determine the area of the polygon. Jan 29-1:27 PM 32

33 2. Plot and connect the points E(-8,8), F(-2,5), and G(-7,2). Then give the best name for the polygon and determine the area. Jan 29-1:28 PM 3. Plot the following points: P(1,-4), Q(5,-2), R(9,-4), S(7,-8), and T(3,-8). Give the best name for the polygon and determine the area. Jan 29-1:28 PM 33

34 4. Jasmine has made a scale drawing of a vegetable garden she plans to make in her backyard. She needs to determine the perimeter and area to know how much fencing and dirt to purchase. Determine both the perimeter and area. Jan 29-1:29 PM 34