1
Name Homeroom MSMM2014
8 cm area = 10 cm area = 10 cm 9 cm area = 7 cm 10 cm area = area = area = 10 cm 10 cm 10 cm MSMM2014 1
Topic: Area of Rectangles and Squares I CAN find the area of rectangles and squares. Find the area of each figure. 1) A = 2) A = 8 cm 12 cm 10 cm You Try It 1) A = 3. 3) A = 4) A = 15 m 2) A = 4 m 4.5 m 8.5 m 5) Jelitza is designing a flower garden. If she makes the garden 18 feet long and 6.2 feet wide, what will the area of the garden be? 3 cm 6) Ben s bedroom is a perfect square, which is 9.5 feet on one side. What is the area of Ben s room? 3) The area of Harold s garden is 42.25 square meters. The width of the garden is 6.5 meters. What is the length? 7) The area of Lynn s room is 123.5 square feet. The length of the room is 13 feet. What is the width? Explain: You can use A = lw or A = s 2 to find the area of a square, but you can t use both to find the area of a rectangle. Why? Give an example to support your answer. 2
Practice: Area of Rectangles and Squares Find each area. 1) A = 2) A = 3) A = 7.5 m 4) A = 10. 5) A = 14 cm 6) A = 4 m 9.1 m 6.3 m 15 m 2.5 m 5 m 7) Paul is designing a flower garden. If he makes the garden 21 feet long and 2.5 feet wide, what will the area of the garden be? 7) 8) Marlee is going to paint her square poster, which is 1.8 meters long. What is the area of the poster? 8) 9) The area of Vaughn s dog pen is 341square feet. The length of the pen is 22 feet. What is the width? 9) 10) Amanda s art project is 48 square inches. What are all the possible dimensions (lengths and widths) of her project? (Sides are whole numbers.) 10) 3
Topic: Area of Triangles I CAN find the area of right triangles and other triangles. Find the area of the triangles. 1) A = 2) A = 12 cm 9 cm You Try It Find the area of the triangles. 1) A = 8 cm 14 cm 3) A = 4) A = 4.6 m 13 m 5) Patrick s abstract art project has a right triangle in it. The base of the triangle is 8 inches and the height is 7.5 inches. What is the area of the triangle? 13 m 5) 22 m 7. 11 cm 2) A = 6) Julie s mom is making a triangular flag to hang outside. The base of the flag is 4 feet and the height is 5.5 feet. What will the area of the flag be? 6) 8 m 7) Samantha is creating a triangular flower garden. The base of the triangle is 7 feet, and she wants the area to be 21 square feet. What does the height need to be? 7) 16.5 m Explain: How are the area of a triangle and the area of a rectangle related? How do their formulas show this? 4
Practice: Area of Triangles Find the area of each triangle. 1) A = 2) A = 1 3) A = 12 m 13 cm 25 m 10. 6. 4) A = 22 m 5) A = 3.2 m 6) A = 9 cm 40 m 14 m 8. 7) Michelle painted a triangle in a mural on her wall. The base of the triangle is 24 inches and the height is 18 inches. What is the area of the triangle? 8) Nancy s dad built a triangular shelf for her. The base of the shelf is 15 inches and the height is 12 inches. What is the area of the shelf? 9) Pedro is designing a kite, and part of it is a triangle. The base of the kite is 20 inches. Pedro wants the area to be 145 square inches. What does the height need to be? 7) 8) 9) 10) A triangle has an area of 30 square meters. Find 3 possible base and height combinations for the triangle. 10) 5
Topic: Area of Special Quadrilaterals I CAN find the area of special quadrilaterals by decomposing into triangles and rectangles. Decomposing shapes: shapes apart into. Find the area of each shape. You Try It Find the area of each shape. 1) 10 cm A = 2) 8 cm A = 1) A = 2 cm 2 cm 7 cm 12 cm 3 cm 3 cm 3) A = 4) A = 2) A = 5. 12 cm 4 cm 9 cm 4 cm 11.5cm Explain: How does the area of a parallelogram compare to the areas of the triangles inside? 6
Practice: Area of Special Quadrilaterals Find the area of each shape, by decomposing the shapes. 1) 4 m 2) 12 cm 3) 1 cm 1 cm 3 cm 3 cm 4.5 m 2. 2. 9. A = A = A = 4) 5) 3. 10 cm 6) 9 cm 8 cm 13 cm 22 cm A = A = A = 7
Topic: Area of Special Quadrilaterals I CAN find the area of special quadrilaterals by using a formula. Area of a parallelogram: Area of a trapezoid: Find the area of each shape. 1) You Try It A = 18 cm 1) A = 2) 8 cm A = 10 cm 7 cm 10 cm 10 cm 3 cm 3 cm 2) A = 3) 5. A = 4) 12 cm A = 7 m 9 m 9 cm 4 cm 3 m Explain: Which method do you prefer for finding the area of a trapezoid decomposing the figure or using the formula? Why? 8
Practice: Area of Special Quadrilaterals Find the area of each shape. Use the parallelogram and trapezoid formulas. 1) 6. 2) 3) 14 cm 2 m 11 cm 6 m 8.5 m 13 cm A = A = A = 4) 5) 9 cm 6) 13 m 9 cm 11 cm 7 m 12 cm 2. 5 m A = A = A = 7) A trapezoid has an area of 45 square centimeters. What could the height and bases be? 9
Practice: Area of Polygons Find the area of each shape. 1) 2) 2 m 14 cm 7 m 21 cm 8 m 11. 12 cm 2 m 12 cm 18 cm A = A = A = 3) 9 cm 10 m 4) 5) 12 m 4 cm 5 m 19 m 12 cm 1 cm 1 cm 1 6) 8 cm 1 1 20 cm A = A = A = 10
Practice: Area of Polygons Find the area of each shape. 1) Steve needs to calculate the area of his living room. Use the diagram to find the area. Area = 7 ft 6 ft 3 ft 2.5 ft living room 10 ft 2.5 ft 3 ft 6 ft 7 ft 2) When Amanda builds her rectangular garden, she s going to use posts in the 4 corners, as part of her fencing. Each post is 0.5 ft by 1 ft. How much area will Amanda have for her plants? 1 ft 0.5 ft 9 ft Area = 1 ft 14 ft 0.5 ft 3) Jill s mom is creating a Halloween flag to hang at the front of their house. How much material will she need to make the flag? 3 ft 1.5 ft 6 ft 2 ft Area = 4) Jerry is fencing in an unusually shaped area for his dog to play in. How much space will his dog have to play? 8.5 ft 10 ft 4 ft Area = 2 ft 2 ft 3.5 ft 11
cut Coordinate Plane plane formed by two that intersect at a right angle one of four regions of the coordinate plane numbered cut cut cut cut fold uses to give a point s location on the axis fold cut the point where the intersect axis 12
Coordinate Plane Quadrants Ordered Pair x-axis Origin y-axis MSMM2014 13
Topic: Polygons on the Coordinate Plane I CAN draw polygons in the coordinate plane given coordinates for the vertices. vertex where edges of a shape meet edge side of 2-D shape Plot each ordered pair. Connect the points to form a polygon, and then name the polygon. 1) (-6, 3), (-1, 3), (-4, 7), (-3, 7) name of polygon 2) (-3, -1), (3, -3), (-3, -3), (3, -1) name of polygon 3) (3, 4), (3, 6), (5, 6), (5, 4) name of polygon 4) (-5, -4), (-6, -7), (-1, -4), (-2, -7) x You Try It Plot each ordered pair. Connect the points to form a polygon, and then name the polygon. 1) (-4, -5), (-3, -3), (0, -3), (1, -5) name of polygon 2) (-4, 3), (-4, 5), (2, 3), (2, 5) name of polygon 3) Write the ordered pairs for the vertices of the square. name of polygon ********************************************** 5) Write the ordered pairs for the vertices of the rectangle. y 6) Write the ordered pairs for the vertices of the trapezoid. 7) Write the ordered pairs for the vertices of the triangle. 8) Three points of a rectangle are (8, 2), (3, 2) and (3, 9). What is the fourth point? Explain: How can you determine a missing point, like in question 8, without using the coordinate plane? 14 MSMM2014
Practice: Polygons on the Coordinate Plane Plot each ordered pair. Connect the points to form a polygon, and then name the polygon. 1) (-5, 2), (-2, 2), (-5, 5), (-2, 5) name of polygon 2) (1, -1), (6, -1), (1, -3), (6, -3) name of polygon 3) (0, 6), (3, 6), (-1, 3), (4, 3) name of polygon 4) (2, -5), (-2, -5), (1, -7), (-3, -7) name of polygon ************************************************************************************* 5) Write the ordered pairs for the vertices of the rectangle. x 6) Write the ordered pairs for the vertices of the trapezoid. 7) Write the ordered pairs for the vertices of the parallelogram. 8) Write the ordered pairs for the vertices of the square. 9) Write the ordered pairs for the vertices of the triangle. y 10) Three points of a rectangle are (6, 4), (3, 4) and (6, 0). What is the fourth point? 11) Three points of a parallelogram are (5, 0), (9, 0), (3, 3). What is the fourth point? 12) Three points of a square are (10, 4), (10, 8), (6, 4). What is the fourth point? 13) Choose ordered pairs to create a shape of your choice (square, rectangle, parallelogram, trapezoid). List the ordered pairs here. MSMM2014 15
Topic: Area of Polygons on the Coordinate Plane I CAN use coordinates to find the lengths of sides and areas of polygons. To find the area of polygons in the coordinate plane, you need to find the found in the. You Try It 1) Shape A is a formula: dimension: dimension: dimension: Area of Shape A = A B 1) Shape C is a formula: dimension: dimension: Area of Shape C = 2) Shape B is a formula: dimension: dimension: Area of Shape B = x C E 2) Shape D is a formula: dimension: 3) Shape E is a formula: dimension: dimension: Area of Shape E = y D dimension: dimension: Area of Shape D = Explain: For some shapes, like rectangles and squares, finding the area on the coordinate plane is easy you can just count the squares! But for others, like parallelograms and trapezoids, counting doesn t work out quite right. Why? 16 MSMM2014
Practice: Area of Polygons on the Coordinate Plane Find the area of each shape. 1) Shape A is a 2) Shape B is a formula: formula: dimension: dimension: dimension: dimension: dimension: A B Area of Shape A = Area of Shape B = x 3) Shape C is a 4) Shape D is a formula: dimension: dimension: Area of Shape C = formula: dimension: dimension: dimension: Area of Shape D = E F y D C 5) Shape E is a 6) Shape F is a formula: formula: dimension: dimension: dimension: dimension: Area of Shape E = Area of Shape F = MSMM2014 17
4 cm Surface Area = Surface Area = s 3 cm 8 cm 3. Surface Area = Surface Area = 12 cm MSMM2014 18
Topic: Surface Area I CAN use nets to find the surface area of figures composed of rectangles and triangles. Use the nets to find the surface area of each figure. You Try It 1) 2) 1) 2 cm 4 cm 3 cm 13 cm 1 3) 10 cm 4) 2) 1 9 cm 8 cm 7 cm Explain: In a triangular prism, there are 2 identical triangles. Instead of finding each triangle using ½bh and multiplying by 2, how else can you find the total area of these 2 triangles? What other way could you calculate the total of the 4 triangles in the square pyramid or triangular pyramid? 19
Practice: Surface Area Using Nets Use the nets to find the surface area of each figure. 1) 2) 3) 2. 1. 3 cm 10 cm 4 cm 12 cm 4) 5. 5) 11 cm 6) 4 cm 7 cm 7 cm 20
Topic: Surface Area Using Formulas I CAN use formulas to find the surface area of figures. Rectangular prism = 2lw + 2lh + 2wh Cube = 6s 2 Triangular prism = bh + aw + bw + cw Square pyramid = s 2 + 4(½bh) Find the surface area of each figure. 1) 2) You Try It 1) 2 cm 4 cm 3 cm 13 cm 20cm 7 cm 4) 5) 10 cm 1 2) 9 cm 8 cm 7 cm 9 cm Explain: Which method do you prefer for finding the surface area using the net to find the area of each part and adding them or using the formula Why? 21
Practice: Surface Area Using Formulas Find the surface area of each figure. 1) 2) 3) 3. 8 cm 11 cm 18 cm 9 cm 10 cm 4) 8 cm 5) 7. 1 12 cm 7 cm 8 cm 6) Mrs. Thomas is wrapping a gift that is 12.5 inches long, 10 inches wide, and 6 inches high. She needs to know the surface area so she can be sure she has enough wrapping paper. What is the surface area of the gift? 22
4 m 22 m 1.5 m height volume is the number of inside a Volume = width length Volume = 2 1 2 cm What is the volume of a cube that has a side length of 1 cm? 2 1 2 cm 1 2 cm 1 2 cm MSMM2014 23
Topic: Volume of Rectangular Prisms I CAN find volumes of right rectangular prisms. Find the volume of each figure. Volume of rectangular = l w h Volume of cube = s 3 You Try It 1) V = 1) V = 8 m 1 2) V = 7 m ½ m 5½ m 3) V = 1 2 7 m 3 m 4) V = 3 ½ cm 3 1 2 cm 3 2) V = 5) V = 4 m 4 6) V = 22 m 1.5 m 4 m 14 cm 4½ cm 5 4 cm 2 cm 6 m 6 7.3 m 3.3 m 3 m 2.1 m 5½ cm 2 cm Explain: Why do both of these formulas work, to find the volume of a cube? V = lwh or V = s 3. Give an example to support your answer. 24
Practice: Volume of Rectangular Prisms Find the volume of each figure. 1) V = 11 cm 1 12 cm 2 2) V = 12 cm 9½ cm ½ cm 3) V = 3 m 3 10.5 m 4 4) V = 3 m 5) V = 2½ m 5 5½ cm 3m 15 m 8 m 6 6) V = 7) V = 3 m 20 m 7 2 m 10 m 8) Mark got fish and a fish tank for his birthday. The tank is 24½ inches long, 12½ inches high and 12 inches wide. What is its volume? V = 25
26