1.7 Find Perimeter, Circumference,


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1 .7 Find Perimeter, Circumference, and rea Goal p Find dimensions of polygons. Your Notes FORMULS FOR PERIMETER P, RE, ND CIRCUMFERENCE C Square Rectangle side length s length l and width w P 5 P 5 s 5 5 Triangle Circle side lengths a, b, radius r a c and c, base b, h C 5 and height h. 5 P 5 5 b Pi (π) is the ratio of a circle's circumference to its diameter. r w Example Find the perimeter and area of a rectangle Tennis The inbounds portion of a singles tennis court is shown. Find its perimeter and area. Perimeter rea P 5 2l 2w 5 lw 5 2( ) 2( ) 5 ( ) 5 5 The perimeter is ft and the area is ft ft 78 ft Checkpoint Complete the following exercise.. In Example, the width of the inbounds rectangle increases to 36 feet for doubles play. Find the perimeter and area of the inbounds rectangle. 24 Lesson.7 Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.
2 .7 Find Perimeter, Circumference, and rea Goal p Find dimensions of polygons. Your Notes FORMULS FOR PERIMETER P, RE, ND CIRCUMFERENCE C Square side length s P 5 4s 5 s 2 s Rectangle length l and width w P 5 2l 2w 5 lw Triangle Circle side lengths a, b, radius r a c and c, base b, h C 5 2πr and height h. 5 πr 2 P 5 a b c b Pi (π) is the ratio of a 5 } 2 bh circle's circumference to its diameter. r w Example Find the perimeter and area of a rectangle Tennis The inbounds portion of a singles tennis court is shown. Find its perimeter and area. Perimeter rea P 5 2l 2w 5 lw 5 2( 78 ) 2( 27 ) 5 78 ( 27 ) The perimeter is 20 ft and the area is 206 ft ft 78 ft Checkpoint Complete the following exercise.. In Example, the width of the inbounds rectangle increases to 36 feet for doubles play. Find the perimeter and area of the inbounds rectangle. perimeter: 228 ft, area: 2808 ft 2 24 Lesson.7 Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.
3 Your Notes The approximations 3.4 and } 22 7 are commonly used as approximations for the irrational number π. Unless told otherwise, use 3.4 for π. Example 2 rchery The smallest circle on an Olympic target is 2 centimeters in diameter. Find the approximate circumference and area of the smallest circle. First find the radius. The diameter is 2 centimeters, so the radius is } 2 ( ) 5 centimeters. Then find the circumference and area. Use 3.4 for π. P 5 2πr ø 2( )( ) 5 5 πr 2 ø ( ) 2 5 Find the circumference and area of a circle Checkpoint Find the approximate circumference and area of the circle m Example 3 Using a coordinate plane Triangle JKL has vertices J(, 6), K(6, 6), and L(3, 2). Find the approximate perimeter of triangle JKL. Write down your calculations to make sure you do not make a mistake substituting values in the Distance Formula. First draw triangle JKL in a coordinate plane. Then find the side lengths. ecause } JK is horizontal, use the to find JK. Use the to find JL and LK. JK units JL 5 Ï }}} ( 2 ) 2 (2 2 ) 2 5 Ï } ø units LK 5 Ï }}} ( 2 3) 2 ( 2 2) 2 5 Ï } 5 units Then find the perimeter. P 5 JK JL LK ø 5 units. y x Copyright Holt McDougal. ll rights reserved. Lesson.7 Geometry Notetaking Guide 25
4 Your Notes The approximations 3.4 and } 22 7 are commonly used as approximations for the irrational number π. Unless told otherwise, use 3.4 for π. Example 2 Find the circumference and area of a circle rchery The smallest circle on an Olympic target is 2 centimeters in diameter. Find the approximate circumference and area of the smallest circle. First find the radius. The diameter is 2 centimeters, so the radius is } ( 2 ) 5 6 centimeters. 2 Then find the circumference and area. Use 3.4 for π. P 5 2πr ø 2( 3.4 )( 6 ) cm 5 πr 2 ø 3.4 ( 6 ) cm 2 Checkpoint Find the approximate circumference and area of the circle m C ø m; ø m 2 Example 3 Using a coordinate plane Triangle JKL has vertices J(, 6), K(6, 6), and L(3, 2). Find the approximate perimeter of triangle JKL. Write down your calculations to make sure you do not make a mistake substituting values in the Distance Formula. First draw triangle JKL in a coordinate plane. Then find the side lengths. ecause } JK is horizontal, use the Ruler Postulate to find JK. Use the Distance Formula to find JL and LK. JK units y J(,6) K(6, 6) L(3, 2) JL 5 Ï }}} ( 3 2 ) 2 (2 2 6 ) 2 5 Ï } 20 ø 4.5 units LK 5 Ï }}} ( 6 2 3) 2 ( 6 2 2) 2 5 Ï } units Then find the perimeter. P 5 JK JL LK ø units. x Copyright Holt McDougal. ll rights reserved. Lesson.7 Geometry Notetaking Guide 25
5 Your Notes Example 4 Solve a multistep problem Lawn care You are using a roller to smooth a lawn. You can roll about 25 square yards in one minute. bout how many minutes does it take to roll a lawn that is 20 feet long and 75 feet wide? You can roll the lawn at a rate of 25 square yards per minute. So, the amount of time it takes you to roll the lawn depends on its. Step Find the area of the rectangular lawn. rea 5 lw 5 ( ) 5 ft 2 The rolling rate is in square yards per minute. Rewrite the area of the lawn in square yards. There are feet in yard, and 2 5 square feet in one square yard ft 2 p yd2 5 ft 2 yd2 Use unit analysis. Step 2 Write a verbal model to represent the situation. Then write and solve an equation based on the verbal model. Let t represent the total time (in minutes) needed to roll the lawn. rea of lawn (yd 2 ) 5 Rolling rate (yd 2 per min) 3 Total time (min) You can roll about 250 yards in 0 minutes. Use this fact to check that your solution is reasonable for the lawn area you found in Step. It takes about 5 p t Substitute. 5 t Divide each side by. minutes to roll the lawn. 26 Lesson.7 Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.
6 Your Notes Example 4 Solve a multistep problem Lawn care You are using a roller to smooth a lawn. You can roll about 25 square yards in one minute. bout how many minutes does it take to roll a lawn that is 20 feet long and 75 feet wide? You can roll the lawn at a rate of 25 square yards per minute. So, the amount of time it takes you to roll the lawn depends on its area. Step Find the area of the rectangular lawn. rea 5 lw 5 20 ( 75 ) ft 2 The rolling rate is in square yards per minute. Rewrite the area of the lawn in square yards. There are 3 feet in yard, and square feet in one square yard ft 2 p yd ft 2 yd2 Use unit analysis. Step 2 Write a verbal model to represent the situation. Then write and solve an equation based on the verbal model. Let t represent the total time (in minutes) needed to roll the lawn. rea of lawn (yd 2 ) 5 Rolling rate (yd 2 per min) 3 Total time (min) You can roll about 250 yards in 0 minutes. Use this fact to check that your solution is reasonable for the lawn area you found in Step p t Substitute. 8 5 t Divide each side by 25. It takes about 8 minutes to roll the lawn. 26 Lesson.7 Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.
7 Your Notes In Example 5, you may want to make and label a sketch of the triangle. The sketch will not be exact, but it will help you visualize the given information. Example 5 The base of a triangle is 24 feet. Its area is 26 square feet. Find the height of the triangle. 5 Find unknown length rea of a triangle 5 Substitute. 5 Multiply. h 24 ft 5 h Solve for h. The height is feet. Checkpoint Complete the following exercises. 3. Find the perimeter of the triangle shown at the right. y (7, 6) (, ) C(7, 3) x 4. Suppose a lawn is half as long and half as wide as the lawn in Example 4. Will it take half the time to roll the lawn? Explain. Homework 5. The area of a triangle is 96 square inches, and its height is 8 inches. Find the length of its base. Copyright Holt McDougal. ll rights reserved. Lesson.7 Geometry Notetaking Guide 27
8 Your Notes In Example 5, you may want to make and label a sketch of the triangle. The sketch will not be exact, but it will help you visualize the given information. Example 5 The base of a triangle is 24 feet. Its area is 26 square feet. Find the height of the triangle. Find unknown length 5 } bh rea of a triangle } (24)(h) Substitute h Multiply. h 24 ft 8 5 h Solve for h. The height is 8 feet. Checkpoint Complete the following exercises. 3. Find the perimeter of the triangle shown at the right. about 7. units y (7, 6) (, ) C(7, 3) x 4. Suppose a lawn is half as long and half as wide as the lawn in Example 4. Will it take half the time to roll the lawn? Explain. No, it will take a quarter of the time to roll the lawn because it is a quarter of the original area. Homework 5. The area of a triangle is 96 square inches, and its height is 8 inches. Find the length of its base. 24 inches Copyright Holt McDougal. ll rights reserved. Lesson.7 Geometry Notetaking Guide 27
9 Words to Review Give an example of the vocabulary word. Point, line, plane Collinear points Coplanar points Line segment, endpoints Ray Opposite rays Intersection Postulate, axiom Coordinate Distance 28 Words to Review Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.
10 Words to Review Give an example of the vocabulary word. Point, line, plane Collinear points line plane point Coplanar points D D and T are coplanar points. Ray X Y ###$ XY is a ray with initial point X. Intersection P T The intersection of two different lines is a point. and are collinear points. Line segment, endpoints C D } CD is a line segment with endpoints C and D. Opposite rays C If C is between and, then ###$ C and ###$ C are opposite rays. Postulate, axiom postulate, or axiom, is a rule that is accepted without proof. Coordinate Distance x x 2 The coordinates of points and are x and x 2. x x 2 5 x 2 2 x The distance between points and is x 2 2 x. 28 Words to Review Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.
11 etween Congruent segments Midpoint Segment bisector ngle, sides, vertex Measure of an angle cute angle Right angle Obtuse angle Straight angle Copyright Holt McDougal. ll rights reserved. Words to Review Geometry Notetaking Guide 29
12 etween C Point C is between Points and. Midpoint Congruent segments C D } and } CD are congruent. Segment bisector M G M is the midpoint of }. ngle, sides, vertex FG is a segment bisector of }. Measure of an angle C Sides ###$ and ###$ C form. The vertex is. cute angle 408 The measure of is 408. Right angle 08 < m < 908 Obtuse angle m Straight angle 908 < m < 808 m Copyright Holt McDougal. ll rights reserved. Words to Review Geometry Notetaking Guide 29
13 ngle bisector, congruent angles Supplementary angles, linear pair Complementary angles, adjacent angles Vertical angles Polygon, side, vertex Concave, convex ngon Equilateral, equiangular, regular Review your notes and Chapter by using the Chapter Review on pages 6 64 of your textbook. 30 Words to Review Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.
14 ngle bisector, congruent angles C D Supplementary angles, linear pair X ###$ D is an angle bisector of CE. CD and DE are congruent. Complementary angles, adjacent angles E S STX and XTY are supplementary. STX and XTY are a linear pair. Vertical angles T Y R 2 P S QPR and RPS are complementary. QPR and RPS are adjacent. and 2 are vertical angles. Polygon, side, vertex Concave, convex polygon side vertex CD is concave. FGHJ is convex. F J D H C G ngon n ngon is a polygon with n sides. Equilateral, equiangular, regular The polygon is equilateral and equiangular, so it is regular. Review your notes and Chapter by using the Chapter Review on pages 6 64 of your textbook. 30 Words to Review Geometry Notetaking Guide Copyright Holt McDougal. ll rights reserved.
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