Slide 1 / 81 Slide 2 / 81 2D Geometry Part 2: Area Rectangles Parallelograms Triangles Trapezoids Circles Mixed Review Irregular Shapes Shaded Regions Click on a topic to go to that section Slide 3 / 81 Slide 4 / 81 Area - The number of square units (units 2 ) it takes to cover the surface of a figure. ALWAYS label units 2!!! Rectangles 12 ft 6 ft Slide 5 / 81 Slide 6 / 81 How many 1 ft 2 tiles does it take to cover the rectangle? Use the squares to find out! Look for a faster way than covering the whole figure. 12 ft The Area (A) of a rectangle is found by using the formula: A = length(width) A = lw The Area (A) of a square is found by using the formula: A = side(side) A = s 2 6 ft
Slide 7 / 81 Slide 8 / 81 1 What is the Area (A) of the figure? 2 Find the area of the figure below. 15 ft 7 6 ft Slide 9 / 81 Slide 10 / 81 3 Dr. Dan wants to keep his kitten from running through his flower bed by putting up some fencing. The flower bed is 10 ft. by 6ft. Will Dr. Dan need to know the area or the perimeter of his flower bed to keep his kitty from trampling the flowers? A Area 4 Now solve the problem... Dr. Dan wants to keep his kitten from running through his flower bed by putting up some fencing. The flower bed is 10 ft. by 6ft. How much fencing will he need? B Perimeter Slide 11 / 81 Slide 12 / 81 Area of a Parallelogram Let's use the same process as we did for the rectangle. How many 1 ft 2 tiles fit across the bottom of the parallelogram? Parallelograms
Slide 13 / 81 Slide 14 / 81 Area of a Parallelogram. How does this help us find the area of the parallelogram? Let's use the same process as we did for the rectangle. If we build the parallelogram with rows of 14 ft 2, what happens? 5 ft 14 ft 14 ft How do you find the area of a parallelogram? How tall is the parallelogram? How can you tell? Slide 15 / 81 Slide 16 / 81 Example. The Area (A) of a parallelogram is found by using the formula: Find the area of the figure. A = base(height) A = bh Note: The base & height always form a right angle! 4 cm 2.2 cm 2.2 cm 1.9 cm 4 cm Slide 17 / 81 Slide 18 / 81 Try These. Find the area of the figures. 11 m 5 Find the area. 8 5 7 20 m 14 m 11 ft 10 ft 11 m 12 ft
Slide 19 / 81 Slide 20 / 81 6 Find the area. 7 Find the area. 17 in 7 m 12 in 10 in 12 in 13 m 13 m 11 m 17 in 7 m Slide 21 / 81 Slide 22 / 81 8 Find the area. 12 cm 11 cm 9 cm Triangles Slide 23 / 81 Area of a Triangle Let's use the same process as we did for the rectangle & parallelogram. How many 1 ft 2 tiles fit across the bottom of the triangle? Slide 24 / 81 Area of a Triangle If we continue to build the triangle with rows of 10 ft 2, what happens? 10 ft How tall is the triangle? How can you tell?
Slide 25 / 81 How does this help us find the area of the triangle? Is this true for all triangles? Let's see! Slide 26 / 81 4 ft 10 ft See that the rectangle we built is twice as large as the triangle. How do you find the area of a triangle? Calculating base(height) results in 2 triangles! 14 ft Slide 27 / 81 The Area (A) of a triangle is found by using the formula: Example. Find the area of the figure. Slide 28 / 81 Note: The base & height always form a right angle! 4 cm 10 cm 10 cm 6 cm Slide 29 / 81 Slide 30 / 81 Try These. Find the area of the figures. 9 Find the area. 13 ft 9 ft 12 ft 14 16 20 11 in 8 in 10 in 11 ft 15 5 in
Slide 31 / 81 Slide 32 / 81 10 Find the area 9 m 8 m 12 m Trapezoids 15 m Slide 33 / 81 Area of a Trapezoid Cut the trapezoid in half horizontally Rotate the top half so it lies next to the bottom half A parallelogram is created Slide 34 / 81 The Area (A) of a trapezoid is found by using the formula: See the diagrams below Base 1 Height Note: The base & height always form a right angle! Base 2 Base 2 Base 1 Slide 35 / 81 Slide 36 / 81 Example. Find the area of the figure. Try These. Find the area of the figures. 12 cm 13 ft 15 10 cm 11 cm 11 ft 9 ft 11 ft 11 ft 9 7 11 20 9 cm
Slide 37 / 81 Slide 38 / 81 11 Find the area of the trapezoid. 12 Find the area of the trapezoid. 4 m 22 cm 6.5 m 8 cm 10 m 14 cm Slide 39 / 81 Slide 40 / 81 Area of a Circle The Area (A) of a Circle is found by solving the following formula: Circles Slide 41 / 81 Slide 42 / 81 7 cm Find the area of the circle. A = # r 2 1. Substitute the radius into formula. A = # (7) 2 2. Use 3.14 as an approximation for #. A = 3.14(49) A = 153.86 cm 2 3. Don't forget to label the units as square units. 13 What is the Area (A) of a Circle with a radius (r) of 8 m? 8 m
Slide 43 / 81 14 What is the Area (A) of the circle? Slide 44 / 81 15 What is the Area (A) of the circle? Slide 45 / 81 16 A circular sprinkler sprays water with a radius of 11 ft. How much area can the sprinkler cover? Slide 46 / 81 17 What is the area of a circle with a diameter of 24 yds? Slide 47 / 81 18 What is the radius of a circle whose area is 254.34 mm 2? Slide 48 / 81 19 A circular pool has an area of 153.86 ft 2. What is its diameter?
Slide 49 / 81 Slide 50 / 81 Mixed Review: Perimeter, Circumference & Area 20 Find the perimeter of the figure. 5 cm 4 cm 3 cm 4 cm 11 cm 21 Find the area of the figure. Slide 51 / 81 Slide 52 / 81 22 Find the perimeter of the figure. 8 yd 9 yd 4 yd 8 yd 4 m 7 m Slide 53 / 81 Slide 54 / 81 23 Find the circumference of the figure. 24 Find the area of the figure. 9 in 5 in 12 in 12 in
Slide 55 / 81 Slide 56 / 81 25 Find the area of the figure. 26 Find the perimeter of the figure. 5 cm 4 cm 3 cm 4 cm 9 in 5 in 12 in 11 cm Slide 57 / 81 Slide 58 / 81 27 Find the perimeter of the figure. 28 Find the area of the figure. 8 yd 4 yd 8 yd 12 in 9 yd Slide 59 / 81 Slide 60 / 81 29 Find the area of the figure. 4 m 7 m
Slide 61 / 81 Slide 62 / 81 Area of Irregular Figures Method #1 Irregular Figures 1. Divide the figure into smaller figures (that you know how to find the area of) 2. Label each small figure and find the area of each 3. Add the areas 4. Label your answer Slide 63 / 81 Slide 64 / 81 Example: Find the area of the figure. 3 m 2 m 10 m 6 m Area of Irregular Figures Method #2 1. Create one large, closed figure. 2. Label the small added figure and find the area. 3 m 3. Find the area of the new, large figure 2 m #1 #2 10 m 6 m 4. Subtract the areas 5. Label your answer Slide 65 / 81 Slide 66 / 81 Example: Find the area of the figure. 3 m 2 m Try These: Find the area of each figure. 3 m 2 m 6 m Whole Rectangle 10 m 6 m Extra Rectangle 2m 4m 5m 2m 10 ft 20 ft 8 ft 16 ft 10 m
Slide 67 / 81 Slide 68 / 81 30 Find the area. Top Rectangle 31 Find the area. 2.5' 2.5' 5.25' 4' 1.5' 8.75' Bottom Rectangle Vertical Rectangle Total Area 25 16 12 19 35 13 Whole New Figure New Rectangle Total Area 7.75' Slide 69 / 81 Slide 70 / 81 32 Find the area. 33 Find the area. Side Rectangle 8 cm 58 cm Triangle 4 ft. Bottom Right Rectangle 15 cm 5 ft. Rectangle 9 ft. Half Circle Total Area 6 ft. Total Area Slide 71 / 81 Slide 72 / 81 Area of a Shaded Region 1. Find area of whole figure. Shaded Regions 2. Find area of unshaded figure(s). 3. Subtract unshaded area from whole figure. 4. Label answer with units 2
Slide 73 / 81 Slide 74 / 81 Example Try This Find the area of the shaded region. 20 ft Area Whole Rectangle Find the area of the shaded region. Area Whole Square 7 ft 7 ft 15 ft Area Unshaded Square Area Circle Area Shaded Region 14 cm Area Shaded Region Slide 75 / 81 Slide 76 / 81 Try This Find the area of the shaded region. Area Trapezoid 34 Find the area of the shaded region. Area Whole Rectangle 20 m 3 m 12 m Area Rectangle 6' 2' 4' Area Unshaded 8 m 2 m Area Shaded Region Area Shaded Region 8' Slide 77 / 81 Slide 78 / 81 35 Find the area of the shaded region. 36 Find the area of the shaded region. Area Parallelogram 8" Area Whole 11" 8" 7" 6" Area Triangle 14" 8" 4" 6" Area Rectangle 12" Area Shaded Region 12" Area Shaded Region
Slide 79 / 81 Slide 80 / 81 37 Find the area of the shaded region. Area Circle 38 A cement path 3 feet wide is poured around a rectangular pool. If the pool is 15 feet by 7 feet, how much cement was needed to create the path? Area Path & Pool 4 yd Area Triangle Area Pool Area Shaded Region Area Path Slide 81 / 81