Slide 1 / 81 2D Geometry Part 2: Area Table of Contents Slide 2 / 81 Rectangles Parallelograms Triangles Trapezoids Circles Mixed Review Irregular Shapes Shaded Regions Click on a topic to go to that section Slide 3 / 81 Rectangles Return to Table of Contents
Area - The number of square units (units 2 ) it takes to cover the surface of a figure. Slide 4 / 81 ALWAYS label units 2!!! 12 ft 6 ft How many 1 ft 2 tiles does it take to cover the rectangle? Slide 5 / 81 Use the squares to find out! Look for a faster way than covering the whole figure. 12 ft 6 ft The Area (A) of a rectangle is found by using the formula: Slide 6 / 81 A = length(width) A = lw The Area (A) of a square is found by using the formula: A = side(side) A = s 2
1 What is the Area (A) of the figure? Slide 7 / 81 15 ft 6 ft 2 Find the area of the figure below. Slide 8 / 81 7 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? Slide 9 / 81 A B Area Perimeter
4 Now solve the problem... Slide 10 / 81 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? Slide 11 / 81 Parallelograms Return to Table of Contents Area of a Parallelogram Slide 12 / 81 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?
Area of a Parallelogram. Slide 13 / 81 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? 14 ft How tall is the parallelogram? How can you tell? How does this help us find the area of the parallelogram? Slide 14 / 81 5 ft 14 ft How do you find the area of a parallelogram? Slide 15 / 81 The Area (A) of a parallelogram is found by using the formula: A = base(height) A = bh Note: The base & height always form a right angle!
Example. Slide 16 / 81 Find the area of the figure. 4 cm 2.2 cm 2.2 cm 1.9 cm 4 cm click to reveal Try These. Find the area of the figures. 11 m Slide 17 / 81 8 5 7 20 m 14 m 11 m click to reveal click to reveal 5 Find the area. Slide 18 / 81 11 ft 10 ft 12 ft
6 Find the area. Slide 19 / 81 17 in 12 in 10 in 12 in 17 in 7 Find the area. Slide 20 / 81 7 m 13 m 13 m 11 m 7 m 8 Find the area. Slide 21 / 81 12 cm 11 cm 9 cm
Slide 22 / 81 Triangles Return to Table of Contents Area of a Triangle Slide 23 / 81 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? Area of a Triangle Slide 24 / 81 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?
How does this help us find the area of the triangle? Slide 25 / 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? 14 ft Is this true for all triangles? Let's see! Slide 26 / 81 Calculating base(height) results in 2 triangles! The Area (A) of a triangle is found by using the formula: Slide 27 / 81 Note: The base & height always form a right angle!
Example. Slide 28 / 81 Find the area of the figure. 4 cm 10 cm 10 cm click to reveal 6 cm Try These. Slide 29 / 81 Find the area of the figures. 13 ft 9 ft 12 ft 14 16 20 11 ft 15 click to reveal click to reveal 9 Find the area. Slide 30 / 81 11 in 8 in 10 in 5 in
10 Find the area Slide 31 / 81 9 m 8 m 12 m 15 m Slide 32 / 81 Trapezoids Return to Table of Contents Area of a Trapezoid Slide 33 / 81 Cut the trapezoid in half horizontally Rotate the top half so it lies next to the bottom half A parallelogram is created See the diagrams below Base 1 Height Base 2 Base 2 Base 1
Slide 34 / 81 The Area (A) of a trapezoid is found by using the formula: Note: The base & height always form a right angle! Example. Slide 35 / 81 Find the area of the figure. 12 cm 10 cm 11 cm click to reveal 9 cm Try These. Slide 36 / 81 Find the area of the figures. 11 ft 13 ft 9 ft 11 ft 11 ft 15 9 7 11 20 click to reveal click to reveal
11 Find the area of the trapezoid. Slide 37 / 81 4 m 6.5 m 10 m 12 Find the area of the trapezoid. Slide 38 / 81 22 cm 8 cm 14 cm Slide 39 / 81 Circles Return to Table of Contents
Area of a Circle Slide 40 / 81 The Area (A) of a Circle is found by solving the following formula: Slide 41 / 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? Slide 42 / 81 8 m
14 What is the Area (A) of the circle? Slide 43 / 81 15 What is the Area (A) of the circle? Slide 44 / 81 16 A circular sprinkler sprays water with a radius of 11 ft. How much area can the sprinkler cover? Slide 45 / 81
17 What is the area of a circle with a diameter of 24 yds? Slide 46 / 81 18 What is the radius of a circle whose area is 254.34 mm 2? Slide 47 / 81 19 A circular pool has an area of 153.86 ft 2. What is its diameter? Slide 48 / 81
Slide 49 / 81 Mixed Review: Perimeter, Circumference & Area Return to Table of Contents 20 Find the perimeter of the figure. Slide 50 / 81 5 cm 4 cm 3 cm 4 cm 11 cm 21 Find the area of the figure. Slide 51 / 81 8 yd 4 yd 8 yd 9 yd
22 Find the perimeter of the figure. Slide 52 / 81 4 m 7 m 23 Find the circumference of the figure. Slide 53 / 81 12 in 24 Find the area of the figure. Slide 54 / 81 9 in 5 in 12 in
25 Find the area of the figure. Slide 55 / 81 5 cm 4 cm 3 cm 4 cm 11 cm 26 Find the perimeter of the figure. Slide 56 / 81 9 in 5 in 12 in 27 Find the perimeter of the figure. Slide 57 / 81 8 yd 4 yd 8 yd 9 yd
28 Find the area of the figure. Slide 58 / 81 12 in 29 Find the area of the figure. Slide 59 / 81 4 m 7 m Slide 60 / 81
Slide 61 / 81 Irregular Figures Return to Table of Contents Area of Irregular Figures Method #1 Slide 62 / 81 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 Example: Find the area of the figure. 3 m 2 m 10 m 6 m Slide 63 / 81 3 m 2 m #1 #2 6 m 10 m
Area of Irregular Figures Method #2 Slide 64 / 81 1. Create one large, closed figure. 2. Label the small added figure and find the area. 3. Find the area of the new, large figure 4. Subtract the areas 5. Label your answer Example: Find the area of the figure. 3 m 2 m Slide 65 / 81 6 m 10 m 3 m 2 m Whole Rectangle Extra Rectangle 6 m 10 m Try These: Find the area of each figure. Slide 66 / 81 2m 8 ft 4m 20 ft 5m 2m 10 ft 16 ft
30 Find the area. Top Rectangle Slide 67 / 81 2.5' 4' Bottom Rectangle 5.25' 1.5' 8.75' Vertical Rectangle 2.5' Total Area 7.75' 31 Find the area. 16 Whole New Figure Slide 68 / 81 25 12 19 13 New Rectangle 35 Total Area 32 Find the area. 8 cm 58 cm Triangle Slide 69 / 81 15 cm Rectangle Total Area
33 Find the area. 4 ft. 5 ft. 9 ft. Side Rectangle Bottom Right Rectangle Half Circle Slide 70 / 81 6 ft. Total Area Slide 71 / 81 Shaded Regions Return to Table of Contents Area of a Shaded Region Slide 72 / 81 1. Find area of whole figure. 2. Find area of unshaded figure(s). 3. Subtract unshaded area from whole figure. 4. Label answer with units 2
Example Slide 73 / 81 Find the area of the shaded region. 20 ft Area Whole Rectangle 7 ft 7 ft 15 ft Area Unshaded Square Area Shaded Region Try This Slide 74 / 81 Find the area of the shaded region. Area Whole Square Area Circle 14 cm Area Shaded Region Try This Find the area of the shaded region. Area Trapezoid Slide 75 / 81 20 m 3 m 12 m Area Rectangle 8 m 2 m Area Shaded Region
34 Find the area of the shaded region. Area Whole Rectangle Slide 76 / 81 6' 2' 4' Area Unshaded Area Shaded Region 8' 35 Find the area of the shaded region. Area Parallelogram Slide 77 / 81 11" 8" 7" 6" Area Triangle 12" Area Shaded Region 36 Find the area of the shaded region. 8" Area Whole Slide 78 / 81 14" 8" Area Rectangle 4" 6" 12" Area Shaded Region
37 Find the area of the shaded region. Area Circle Slide 79 / 81 4 yd Area Triangle Area Shaded Region 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 Slide 80 / 81 Area Pool Area Path Slide 81 / 81