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Course 1 Unit 9AreaName: ___________________Lesson 9-1: Area of Parallelogramspolygon – _______________________________________________________________________________________________________________________parallelogram – __________________________________________________________________________________________________________________rhombus – _______________________________________________________________________________________________________________________Venn Diagram:Example 1Find the area of the parallelogram. The base is 6 units, and the height is 8 units.4680403-508000A = bhA = ____ · _____A = ____________ square units or ______ units?Example 2Find the area of the parallelogram.432716985000A = bh A = ____ · _____ A = ______ ______ square units or ______ units?Got it? 439782821027500Find the area of each parallelogram.239395-1270001.2. Finding the HeightThe formula to find the height is this…Height = Area ÷ baseOrHeight = AreaBase389654115221800Example 3Find the missing dimension of the parallelogram. height = area ÷ base height = _______ ÷ _______ height = _______ inchesGot it? 389636023304500Find the missing dimension of the parallelogram.26098543180003.4. Example 4Romilla is painting a replica of the national flag of Trinidad and Tobago for a research project. Find the area of the black stripe.12 (634)634 = ___________12 (274) = 121 · 274 = ___________= _____ sq. in.Guided Practice:38421132317750023876023368000Find the area of each parallelogram.1. 2. 3. Find the height of a parallelogram if its base is 35 centimeters and its area is 700 square centimeters. 4. What two formulas can you use when finding the height of a parallelogram? 5. What two basic shapes make up a parallelogram? 6. Draw a parallelogram with an area of 24 square inches. (There are many answers.)Lesson 9-2 Area of Trianglescongruent – _____________________________________________________________________________________________________________________**They are ______________________ the same**Example 16413522479000Find the area of the triangle.A = 12?· ______ · ______A = 12 · ______A = ______ units?Example 2Find the area of the triangle.0498900A = ? bhA = 12?· ______ · ______A = 12 · ______A = ______ m?Got it? 40476712254250023241022542500Find the area of each triangle.1. 2. Finding the Base or Height:base = 2(Area) ÷ heightheight = 2(Area) ÷ baseExample 3419027411747500Find the missing dimension of the triangle.base = 2(Area) ÷ heightbase = 2(______) ÷ _______base = ________ ÷ _______base = ________ cmGot it? Find the missing side length for each triangle.Formulas: base = 2(Area) ÷ height height = 2(Area) ÷ base3874770-254000184785-2540003. 4. Example 4The front of a camping tent has the dimensions 5ft by 3ft. How much material was used to make the front of the tent?A = 12(______)(______)A = 12(______)A = _______A = ________ sq. ft.Guided Practice: Find the area. Find the base.3875042635001. 184785635002. 3. Compare and contrast the formula for a parallelogram to the formula for the area of a triangle. What do they have in common? What is different? Lesson 9-3: Area of TrapezoidsExample 1412496022669500Find the area of the trapezoid.A =(b1+b2)h2A =(5+12)72A = (___________)72A = _____________2A = ________ in?Example 2:Find the area of the trapezoid.2159015367000A =(b1+b2)h2A =(7+12)9.82A = (___________)9.82A = _____________2A = ________ in?261220924257000Got it? 48025058255001847858890001. 2. 3. To Find the Height…The formula for finding the height ish=?2(Area)b1+b2Orh=2Area÷(b1+b2)462597523939500Example 3The trapezoid has an area of 108 square feet. Find the height.h=2Area÷(b1+b2)h=2_________÷(_________+__________)h=_____________÷(____________)h=_____feetGot it? 4. A = 24cm?b1= 4cmb2 = 12cmh = ?5. A = 21yd?b1= 2ydb2 = 5ydh = ?Example 4The shape of Osceola County, Florida, resembles a trapezoid. Find the approximate area of this county.A =(b1+b2)h2A = (48?+?16)51?2A =(___________)______________?2A = ____________________2A = ________ miles?Guided Practice:Find the area of the trapezoid.Find the height of the trapezoid.2281465292001. 2. Area = 15 square feet base 1 = 4 feet base 2 = 6 feet height = ?3. Compare and contrast the formula for a parallelogram to the formula for the area of a trapezoid. What do they have in common? What is different? 47879025527000Lesson 9-4 Changes in Dimension501777010922000Example 1Suppose the side lengths of the parallelogram at the right are tripled.What effects would this have on the perimeter? Side ASide BPerimeter343 + 3 + 4 + 4 = 14 inchesTripled (Multiplied by 3)_______ ÷ 14 = _______The perimeter is _______ times bigger. Got it? 4559529346801001. Suppose the side lengths of the trapezoid at the right are multiplied by 12. What effect would this have on the perimeter? TopSideBottomPerimeterHalved (Multiplied by ?)_______ ÷ _______ = _______The perimeter is _______ times bigger. 5397518278900470154021717000Example 2The side lengths of the triangle at the right are multiplied by 5. What effect would this have on the area? BaseHeightArea21A = ? (2)(1) = 1 cm2Multiplied by 5_______ ÷ 1 = _______The area is _______ times bigger. Got it? 2. A rectangle measures 2 feet by 4 feet. Suppose the side lengths are multiplied by 2.5. What effect would this have on the area? BaseHeightAreaMultiplied by 2.5_______ ÷ ________ = _______The area is _______ times bigger. Example 3-14097042989500A stop sign is in the shape of a regular octagon. Sign A shown at the right has an area of 309 square inches. What is the area of sign B?Since 12 ÷ 8= _______The area is 309(_______?).309 (______) =____________ in?Got it? 3. Different sizes of regular hexagons are used in a quilt. Each small hexagon has side lengths of 4 inches and an area of 41.6 square inches. Each large hexagon has side lengths of 8 inches. What is the area of each large hexagon?Hint: 8 ÷ 4 = 2, so the large is twice as big as the small.4505960000Guided Practice:1. Each side length is doubled. Describe the change in perimeter. BaseHeightPerimeterMultiplied by ______465836035560002. Each side length is tripled. Describe the change in area.BaseHeightAreaMultiplied by ______Lesson 9-5: Polygons on the Coordinate Plane482219015846600Example 1A rectangle has vertices A(2, 8), B(7, 8), C(7, 5), and D(2, 5). Use the coordinates to find the length of each side. Then find the perimeter of the rectangle.Find the lengths of the sides, which are shown.Add up 5 + 5 + 3 + 3.______ unitsExample 2Rectangle ABCD has vertices A(2, 1), B(2, 5), C(4, 5), and D(4, 1). 45294556477000Use the coordinates to find the length of each side. Then find the perimeter of the rectangle.Use graph paper. P = 2 + 2 + 4 + 4P = ______ unitsGot it? Use the coordinates to find the length of each side. Then find the perimeter of the rectangle.163286471805001. E(3, 6), F(3, 8), G(7, 8), H(7, 6)2. I(1, 4), J(1, 9), K(8, 9), L(8, 4)3374390507090046699722394100Example 3Each grid square on the zoo map has a length of 200 feet. Find the total distance, in feet, around the zoo.Find the perimeter.10 + 7 + 7 + 3 + 3 + 4 + 4 + 4 = 42 units.Multiply by ______ to find the total feet.______ x ______ = __________ feetGot it? 3. The coordinates of the vertices of a garden are (0, 1), (0, 4), (8, 4), and (8, 1). If each unit represents 12 inches, find the perimeter in inches of the garden.Example 4Find the area of the figure in square units.The figure can be separated into a rectangle and a trapezoid.Area of rectangle:2 x 5 = ______ units2Area of trapezoid:(3+4)(2)2 = _____ units248408771914000Total: _______ + ________ = _______ units2Got it? 4. Find the area, in square units, of the figure.Example 5428897129164600A figure has vertices A(2, 5), B(2, 8), and C(5, 8). Graph the figure and classify it. Then find the area.B = _____ unitsH = _____ unitsA = 3(3)2 = 92or ______ units2This figure is a _______________.42875208382000Got it? 5. Graph the figure and classify it. Then find the area. A(3, 3), B(3, 6), C(5, 6), D(8, 3)Guided Practice:Use the coordinates to find the length of each side. Then find the perimeter of the rectangle.1. L(3,3), M(3,5), N(7,5), P(7,3)2. P(3,0), Q(6,0), R(6,7), S(3,7)3860800736600026924068580003. Mrs. Piel is building a fence around the perimeter of heryard for her dog. The coordinates of the vertices of the yard are (0,0), (0,10), (5,10), and (5,0). If each grid square is has a length of 100 feet, find the amount of wire, in feet, needed for the fence. 4. What is the shape of her yard? Lesson 9-6: Area of Composite Figures composite figure – ________________________________________________________________________________________________________________Example:445679312319000Example 1Find the area of the image. Area = 6 x 10Area = ? x 4 x 4 Area = _______ Area = ________Total Area = ______ + ______ or _______ inches square34194752387600019594423975800Got it? 1. 2. Example 2Find the area of the pool’s floor.Separate the figure into a rectangle and a trapezoid.Rectangle: 28 x 14 =Trapezoid: (4?+?6)22= 202 = Area = ____________Area = ____________Total: __________ + __________ = _______________ft.2Got it?Find the area of the figure below.19558085090003. 4467770878700Example 3Find the area of the figure at the right.Find the area of the square and the rectangle.Square: 12(12) = _______ sq. cm.Rectangle: 15(12) = _______ sq. cm.Add: _______ + _______ =_______Find the area of the overlapping section:_______ x _______= 42 sq. cm.Subtract: _______ – 42 = _______ sq. cm.Got it? 4. Find the area of the figure. Example 4Charlie and Matthew are neighbors in an apartment complex where they share the same patio. What is the area of both apartments and the patio?441198013208000Each apartment is the same:One Apartment: 55(45) = _______Double it: _______+ _______= _______ft2What is the length of each side of the patio?55ft – 32ft = _______ftArea of the patio:23(23) = _______ft2_______– _______ = _______sq. ft.Guided Practice:1. Why is it important to understand the formulas for area of a parallelogram, triangle, and trapezoid when finding the area of composite figures? Write your answer in complete sentences. ................
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