Lesson 1 Area of Parallelograms
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1 NAME DATE PERIOD Lesson 1 Area of Parallelograms Words Formula The area A of a parallelogram is the product of any b and its h. Model Step 1: Write the Step 2: Replace letters with information from picture or model. Step 3: Solve using your knowledge of Example 1 Find the area of the parallelogram. The base is units, and the height is units. Example 2 Find the height of the parallelogram. Example 3: TO FIND THE AREA OF SHADED REGION 1. Find area of bigger parallelogram 2. Find area of smaller parallelogram 3. Subtract the two areas
2 NAME DATE PERIOD Find the area of each parallelogram Find the height of a parallelogram if its base is 9 feet and its area is 27 square feet.
3 NAME DATE PERIOD Lesson 1 Homework Practice Area of Parallelograms Find the area of each parallelogram Find the area of the shaded region in each figure. 6.
4 NAME DATE PERIOD Lesson 1 Area of Parallelograms Words Formula The area A of a parallelogram is the product of any base b and its height h. A = bh Model Step 1: Write the formula Step 2: Replace letters with information from picture or model. Step 3: Solve using your knowledge of equations Example 1 Find the area of the parallelogram. A = bh Area of parallelogram A = 4 7 Replace b with 4 and h with 7. A = 28 Multiply. The area is 28 square units or 28 units 2. The base is 4 units, and the height is 7 units. Example 2 Find the height of the parallelogram. A = bh Area of parallelogram 24 = 6 h Replace A with 24 and b with = 6h 6 Divide each side by 6. 4 = h Simplify. So, the height is 4 inches.
5 Lesson 2 & 3 Area of Triangles Words Symbols The area A of a triangle is one half the product of any base b and its height h. A= 1 2 b x h Model Examples 1. Find the area. 2. Find the height. MS. SIHKSNEL S RULE! YOU MUST MUST MUST write the formula for the figure when solving any geometry problem. Area of Trapezoids A trapezoid has two bases, b1 and b2. The height of a trapezoid is the distance between the two bases. The area A of a trapezoid equals half the product of the height h and the sum of the bases b 1 and b 2. A= 1 2 h (b1+b2) Example Find the area of the trapezoid.
6 Exercises Find the area of each triangle Find the missing dimension: A = 36 Height = 3 Exercises Find the area of each figure. Round to the nearest tenth if necessary
7 Lesson 2/3 Homework Practice Area of Triangles Find the area of each triangle Find the missing dimension. 3. height: 15 ft 4. base: 17 cm area: 285 ft2 area: 18.7 cm2 Area of Trapezoids Find the area of each figure. Round to the nearest tenth if necessary
8 Lesson 2/3 Area of Triangles Words Symbols The area A of a triangle is one half the product of any base b and its height h. A= 1 2 b x h Model Examples 1. Find the area. 2. Find the height. A = h2 Area of a triangle The measure of the 42 = 14 h2 Replace A with 42 and b with 14. base is 5 units, and the height is 8 units. 42(2) = 14 h2(2) Multiply both sides by 2. A = h2 Area of a triangle 84 = 14 h Simplify. A = 5 82 Replace b with 5 and h with = 14 h14 Divide by 14. A = 402 Simplify the numerator. 6 = h Simplify. A = 20 Divide. The area is 20 square units. The height is 6 meters. Area of Trapezoids A trapezoid has two bases, b1 and b2. The height of a trapezoid is the distance between the two bases. The area A of a trapezoid equals half the product of the height h and the sum of the bases b 1 and b 2. A= 1 2 h (b1+b2) Example Find the area of the trapezoid. A = 12h(b 1 + b 2 ) Area of a trapezoid A = 12 (4)(3 + 6) Replace h with 4, b 1 with 3, and b 2 with 6. A = 12 (4)(9) Add 3 and 6. A = 18 Simplify. The area of the trapezoid is 18 square centimeters.
9 Lesson 4 Changes in Dimension Changing the size of a figure: To make a figure bigger we EACH side by the same number To make a figure bigger we EACH side by the same number To find the of any figure we ADD all sides Example 1 Suppose the side lengths of the rectangle shown at the right are doubled. What effect would this have on the perimeter? 6 ft 4 ft 8 ft Example 2 Refer to Example 1. What effect would the described change have on the area? 12 ft When solving word problems: and the figure Write the correct Substitute and solve. EXAMPLE: What is the base of a parallelogram with height 5.6 meters and an area of 39.2 square meters? Draw : Formula: Solve:
10 Exercises Refer to the figure at the right for Exercises 1 and 2. Justify your answers. 1. Each side length is multiplied by 4. Describe the change in the perimeter Each side length is multiplied by 2. Describe the change in the area. 4. Find the height of a parallelogram with an area of 224 square meters and a base of 16 meters. 5.Find the height of a triangle with an area of 245 square inches and a base of 14 inches.
11 Lesson 4 Homework Practice Changes in Dimension Refer to the figures at the right for Exercises 1 4. Justify your answers. 1. Describe the change in the AREA from Figure A to Figure B. 2. Describe the change in the PERIMETER from Figure C to Figure D. 3. Mrs. Giuntini s lawn is triangle shaped with a base of 25 feet and a height of 10 feet. What is the area of Mrs. Giuntini s lawn? 4. Eric made a sign in the shape of a trapezoid. The base sides measured 18 inches and 35 inches. The height between these sides was 19 inches. What was the area of Eric s sign
12 Lesson 4 Changes in Dimension Changing the size of a figure: To make a figure bigger we MULTIPLY EACH side by the same number To make a figure bigger we DIVIDE EACH side by the same number To find the PERIMETER of any figure we ADD all sides Example 1 Suppose the side lengths of the rectangle shown at the right are doubled. What effect would this have on the perimeter? 6 ft 4 ft The dimensions are two times greater. original perimeter: 2(6) + 2(4) = 20 feet new perimeter: 2(12) + 2(8) = 40 feet Since 40 = 2(20), the perimeter is 2 times the perimeter of the original figure. 12 ft 8 ft Example 2 Refer to Example 1. What effect would the described change have on the area? original area: 6 4 = 24 square feet new area: 12 8 = 96 square feet Since 96 = 4(24), the area is 4 times the area of the original figure. When solving word problems: DRAW and LABEL the figure Write the correct FORMULA Substitute and solve.
13 NAME DATE PERIOD Lesson 5 Polygons on the Coordinate Plane You can use coordinates of a figure to find its dimensions by finding the distance between two points. Step 1: the coordinates Step 2: Count the boxes to find the and the Step 3: To find the perimeter up all the sides Step 4: To find the area- Use the correct Example A rectangle has vertices A(1,1), B(1,3), C(5,3), and D(5,1). Use the coordinates to find the length of each side. Then find the perimeter of the rectangle. Width: Find the length of the horizontal lines. ***Remember how to graph? Over x, Up y Length: Find the length of the vertical lines. Perimeter: Area: Don t forget to label your points! 2. X (2,0), Y(6,0), Z(6,7) Graph and find the area Area
14 NAME DATE PERIOD Exercises Use the coordinates to find the length of each side of the rectangle. Then find the perimeter. 1. R(1,1), S(1,7), T(5,7), U(5,1) 2. E(3,6), F(7,6), G(7,2), H(3,2) Lesson 5 Homework Practice Polygons on the Coordinate Plane Graph each figure and find the area AND perimeter.
15 NAME DATE PERIOD 1. A(5, 6), B(9, 3), C(5, 3) Area: 2. H(3, 0), I(3, 7), J(6, 7), K(6, 0) Perimeter: Area: 4. L( 3, 2), M( 3, 2), N(2, 2), O(2, 2) Perimeter: Lesson 5 Area: Polygons on the Coordinate Plane You can use coordinates of a figure to find its dimensions by finding the distance between two points. Step 1: GRAPH the coordinates
16 NAME DATE PERIOD Step 2: Count the boxes to find the LENGTH and the WIDTH Step 3: To find the perimeter ADD up all the sides Step 4: To find the area- Use the correct FORMULA Example A rectangle has vertices A(1,1), B(1,3), C(5,3), and D(5,1). Use the coordinates to find the length of each side. Then find the perimeter of the rectangle. Width: Find the length of the horizontal lines. AD is 4 units long. BC is 4 units long. Length: Find the length of the vertical lines. AB is 2 units long. DC is 2 units long. Add the lengths of each side to find the perimeter = 12 units So, rectangle ABCD has a perimeter of 12 units. Exercises
17 Lesson 6 Area of Composite Figures To find the area of a composite figure, separate it into figures whose areas you know how to find, and then the areas. Parallelogram Triangle Trapezoid Example Find the area of the figure at the right in square feet. The figure can be separated into a rectangle and a trapezoid. Find the area of each. Shape 1 Shape 2 Sum (Add) Example 2 Shape 1 Shape 2 Sum (Add) Course 1 Chapter 9 Area 143
18 Exercises Find the area of each figure. Round to the nearest tenth if necessary. 1. Shape 1 Shape 2 Sum (Add) 2. Shape 1 Shape 2 Sum (Add) 3. Shape 1 Shape 2 Sum (Add) Course 1 Chapter 9 Area 143
19 Lesson 6 HW Exercises Find the area of each figure. Round to the nearest tenth if necessary. 1. Shape 1 Shape 2 Sum (Add) 2. Shape 1 Shape 2 Sum (Add) 3. Shape 1 Shape 2 Sum (Add) Course 1 Chapter 9 Area 143
20 Lesson 6 Area of Composite Figures To find the area of a composite figure, separate it into figures whose areas you know how to find, and then the areas. Example Find the area of the figure at the right in square feet. The figure can be separated into a rectangle and a trapezoid. Find the area of each. Area of Rectangle A = lw Area of a rectangle. A = 12 8 Replace l with 12 and w with 8. A = 96 Multiply. Area of Trapezoid A = 12h(b 1 + b 2 ) Area of a trapezoid A = 12 (4)(4 + 12) Replace h with 4, b 1 with 4, and b 2 with 12. A = 32 Multiply. The area of the figure is or 128 square feet. Course 1 Chapter 9 Area 143
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