Geometry Warm Ups Chapter 11 Name Period Teacher 1
1.) Find h. Show all work. (Hint: Remember special right triangles.) a.) b.) c.) 2.) Triangle RST is a right triangle. Find the measure of angle R. Show all work. 3.) Find x. Show all work. 2
1.) Sam rode his bike along the path from the library to baseball practice. What type of angle did he form during the ride? 2.) Explain the difference between area and perimeter in your own words. 3.) Find the area and perimeter of the parallelogram. Show all work. 16 yds 60 0 12 yds 4.) The area of a rectangle is 38 square units and the width is 19 units. Find the length of the rectangle. Show all work. 3
1.) Which segments are parallel? Why? (Hint: find the missing angle measures.) 2.) Find x. Show all work. 3.) Explain why area is always units squared (feet squared, miles squared, etc) and perimeter is always units (inches, centimeters, etc.). 4.) Find the area of the quadrilateral. Show all work 4
1.) Find the area of each figure. Show all work. a.) b.) c.) 2.) Find x. Show all work. 3.) Find h. Show all work. a.) b.) 5
1.) Find h. Show all work. a.) b.) 2.) Find the area of each figure. Show all work. a.) b.) 3.) Given a trapezoid with an area of 42.5 square millimeters and bases of 6 millimeters and 11 millimeters, find the height. Show all work. 6
1.) What is the relationship between a radius and a diameter of a circle? 2.) Find the area of the shaded region. Show all work. 8 km 16 km 32 km 3.) Find the area of the figure. Show all work. 7
1.) If angle A and angle E are congruent, find AB, the distance in feet across the pond. Show all work. (Hint: Remember similar triangles and ratios.) 2.) Find the area of each figure. Show all work. a.) b.) 3.) Find the area of the shaded region. Show all work, and leave answer in simplified radical form. 8
1.) Find the area of each figure. Show all work. a.) b.) 2.) The apothem of a regular hexagon is 7.8 centimeters. If the length of each side is 9 centimeters, what is the area of the hexagon? Show all work. 9
1.) Find the area of the figure. Show all work. 2.) Find the area of a regular octagon with a perimeter of 72 inches. Show all work. 1.) Find the area of the shaded region. a.) b.) 10
1.) Find the area of each polygon. Show all work. a.) A regular triangle with a perimeter of 48 feet b.) 11
1.) Find the area of the triangle. Show all work. 2.) Find the area of the shaded region. Show all work. 12
Unit 11 Geometry Area, Perimeter, and Circumference Name: Period: 1
Formula Sheet Use Chapter 8 and 11 as references to complete the chart below Name: Date: Period: Name of Figure Drawing Definition Formula for Area Rectangle Parallelogram Triangle Trapezoid Rhombus Regular Polygon Circle 2
Date: Perimeter and Area of Squares, Rectangles, and Parallelograms Notes Perimeter Area Square: Rectangle: Parallelogram: Find the perimeter and area of the following figures. 1.) 2.) 3.) 4.) 3
5.) 6.) Find the area of the shaded region. 7.) 8.) Find the height of the following parallelogram given its area. 9.) A = 100 square units 10.) The Mysels are planning to recarpet part of the first floor of their house. Find the amount of carpet needed to cover the living room, den, and hall. 4
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Date: Perimeter and Area of Triangles, Trapezoids, and Rhombi Notes Triangle: Trapezoid: Rhombus: Find the perimeter and area of the following figures. 1.) 2.) 3.) 4.) 6
5.) 6.) Trapezoid ABCD has an area of 750 square meters. Find the height of ABCD. 7.) Rhombus MNPQ has an area of 375 square inches. If MP is 25 inches, find NQ. 7
Date: Areas of Circles Notes Circumference: Area: Example #1: Find the areas of the following circles. Example #2: Find the areas of the shaded regions. a.) b.) 8
c.) d.) Find the area of the following figure. 9
Name: Circumference and Area of Circles Worksheet Find the circumference and area of the following figures. 1.) 2.) Find the area of the shaded region. 3.) 4.) 5.) 6.) Find the areas of the following figure. 7.) 10
Areas of Irregular Figures Notes Date: Irregular figure Example #1 Find the area of the figure in square feet. Round to the nearest tenth if necessary. Example #2 A rectangular rose garden is centered in a border of lawn. Find the area of the lawn around the garden in square feet. Example #3 Find the area of each figure. Round to the nearest tenth if necessary. 11
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Name: Use the following description and diagram to answer the questions. You need to show ALL work to get full credit. The shape of a roof as viewed from above is shown in the diagram. The building owner is installing new shingles on the roof. Three bundles of shingles is called a square and covers 100 square feet. Bundles of shingles cost $33 each. An experienced roofer can lay a bundle of shingles in an average of 15 minutes. 18 ft 25 ft 75 10 ft 34 ft 18 ft 1. What is the area of the roof? 2. How many square feet does a bundle of shingles cover? 3. How many bundles of shingles are needed? 4. How many squares of shingles are needed? 5. What is the cost of a bundle of shingles? 13
6. What is the cost of a square of shingles? 7. How long will it take an experienced roofer to lay a square of shingles? 8. How long will it take an experienced roofer to complete the entire job? 9. If the roofer gets paid $30 per hour, how much will she earn for the job? 10. What is the total cost of the job? 14
Name: Show all your work and explain your steps 1. An 18 ft. by 15 ft. swimming pool is to be surrounded by a 3 ft. wide walkway made of concrete. A) Find the area of the walkway and B) What is the cost to make the walkway if the price of concrete is $2.18 per square foot? 2. This stained glass window is composed of 8 congruent trapezoidal shapes. The total area of the design is 72 square feet. Each trapezoid has bases of 3 and 6 feet. Find the height of each trapezoid. Explain your steps. 15
3. The local football team wants to purchase enough tarp material to cover their field during bad weather. The field, including the end zones is 120 yards long and 50 yards wide. They want to get exactly nineteen percent more than is needed to cover the field so some of the sidelines and area beyond end each zone are covered as well. How many square yards of tarp material should they buy? 4. You work for a fencing company. A customer called this morning, wanting to fence in his 1,320 square-foot garden. He ordered 148 feet of fencing, but you forgot to ask him for the width and length of the garden. Because he wants a nicer grade of fence along the narrow street-facing side of his plot, these dimensions will determine some of the details of the order, so you do need the information. But you don't want the customer to think that you're an idiot, so you need to figure out the length and width from the information the customer has already given you. What are the dimensions? 16
5. A goat is tied to the corner of a 5-by-4-meter shed by a 8-meter piece of rope. Rounded to the nearest square meter, what is the area grazed by the goat? 6. Find the largest possible rectangular area you can enclose, assuming you have 128 meters of fencing. What is the (geometric) significance of the dimensions of this largest possible enclosure? 17
7. A circular fountain has a diameter of 10 meters. The statue in the middle has a diameter of 1 meter. What is the area of the bottom of the fountain? 8. What are the dimensions of a square that would cover the same amount of space as a circle with a diameter of 4 meters? 9. What is the distance from one side of an oval track that is 400 meters in total length if each of the two straight sections is 100 meters and each curve is 100 meters? 18
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Geometry Chapter 11 Areas of Circles and Polygons HOMEWORK Name: Period: 1
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11-1 NAME DATE PERIOD Practice Area of Parallelograms Find the perimeter and area of each parallelogram. Round to the nearest tenth if necessary. 1. 2. 3. 5 m 8 cm 60 45 11 m 10 cm 10 in. 45 Find the area of each figure. 4. 1 5. 2 2 4 2 4 1 2 2 4 2 9 3 2 3 3 2 7 3 3 3 2 2 8 7 4 3 1 COORDINATE GEOMETRY Given the coordinates of the vertices of a quadrilateral, determine whether it is a square, a rectangle, or a parallelogram. Then find the area of the quadrilateral. 6. C( 4, 1), D( 4, 2), F(1, 2), G(1, 1) 7. W(2, 2), X(1, 2), Y( 2, 2), Z( 1, 2) 8. M(0, 4), N(4, 6), O(6, 2), P(2, 0) 9. P( 5, 2), Q(4, 2), R(5, 5), S( 4, 5) FRAMING For Exercises 10 12, use the following information. A rectangular poster measures 42 inches by 26 inches. A frame shop fitted the poster with a half-inch mat border. 10. Find the area of the poster. 11. Find the area of the mat border. 12. Suppose the wall is marked where the poster will hang. The marked area includes an additional 12-inch space around the poster and frame. Find the total wall area that has been marked for the poster. Glencoe/McGraw-Hill Glencoe Geometry 5
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11-2 NAME DATE PERIOD Practice Areas of Triangles, Trapezoids, and Rhombi Find the area of each figure. Round to the nearest tenth if necessary. 1. 2. 1.5 m 3.2 m 2.6 m 3.5 cm 6 cm 3 cm 4 m 10 cm 3. 37 ft 22 ft 26 ft Find the area of each quadrilateral given the coordinates of the vertices. 4. trapezoid ABCD 5. rhombus LMNO A( 7, 1), B( 4, 4), C( 4, 6), L(6, 8), M(14, 4), N(6, 0), D( 7, 3) O( 2, 4) Find the missing measure for each figure. 6. Trapezoid WXYZ has an area of 7. Triangle PRS has an area of 13.75 square meters. Find WX. 68 square yards. If the height of PRS is 8 yards, find the base. W 2.5 m X R Z 3.5 m Y P S DESIGN For Exercises 8 and 9, use the following information. Mr. Hagarty used 16 congruent rhombi-shaped tiles to design the midsection of the backsplash area above a kitchen sink. The length of the design is 27 inches and the total area is 108 square inches. 8. Find the area of one rhombus. 9. Find the length of each diagonal. Glencoe/McGraw-Hill Glencoe Geometry 7
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11-3 NAME DATE PERIOD Practice Areas of Regular Polygons and Circles Find the area of each regular polygon. Round to the nearest tenth. 1. a nonagon with a perimeter of 117 millimeters 2. an octagon with a perimeter of 96 yards Find the area of each circle. Round to the nearest tenth. 3. a circle with a diameter of 26 feet 4. a circle with a circumference of 88 kilometers Find the area of each shaded region. Assume that all polygons are regular. Round to the nearest tenth. 5. 6. 12 cm 4.4 in. 7. 8. 25 ft 9 m DISPLAYS For Exercises 9 and 10, use the following information. A display case in a jewelry store has a base in the shape of a regular octagon. The length of each side of the base is 10 inches. The owners of the store plan to cover the base in black velvet. 9. Find the area of the base of the display case. 10. Find the number of square yards of fabric needed to cover the base. Glencoe/McGraw-Hill Glencoe Geometry 9
11-4 NAME DATE PERIOD Practice Areas of Irregular Figures Find the area of each figure. Round to the nearest tenth if necessary. 1. 20 2. 38 20 22 22 3. 4. 9 20 23 7 13 13 30 5. y 6. D(2, 5) E(4, 4) B( 1, 3) C(1, 4) P( 2, 3) y Q(2, 6) R(4, 3) A( 1, 0) O F(4, 0) x T( 2, 1) O S(2, 0) x LANDSCAPING For Exercises 7 and 8, use the following information. One of the displays at a botanical garden is a koi pond with a walkway around it. The figure shows the dimensions of the pond and the walkway. 13 ft 35 ft 7 ft 15 ft 7. Find the area of the pond to the nearest tenth. 8. Find the area of the walkway to the nearest tenth. Glencoe/McGraw-Hill Glencoe Geometry 10
DO NOT REMOVE FROM BOOKLET Formulas that you may need to work questions on this test are found below. You may refer to this page at any time during the mathematics test. You may use calculator or the number 3.14. 2006 Grade 11 w l P 2l 2w A lw l h w SA 2lw 2lh 2wh V lwh c a b Permutations : Pythagorean Theorem : a 2 b 2 c 2 P(n, r) n! (n r)! b h A bh r SA 4 r 2 V 4 3 r 3 Combinations : C(n, r) n! r!(n r)! Distance Formula : d (x 2 x 1 ) 2 (y 2 y 1 ) 2 a h A 1 h(a b) 2 r h SA 2 r 2 2 rh V r 2 h Midpoint : x 1 x 2 2, y 1 y 2 2 b h Slope : m y 2 y 1 x 2 x 1 r c h d P b c d A 1 2 bh SA r 2 r r 2 h 2 V 1 3 r 2 h Point-Slope Formula : (y y 1 ) m(x x 1 ) b Slope-Intercept Formula : y mx b h Standard Equation of a Line : r C 2 r A r 2 base SA (Area of the base) 1 2 (number of base sides)(b) b Ax By C V 1 3 (Area of the base) h Copyright 2005 by the Pennsylvania Department of Education. The materials contained in this publication may be duplicated 550548-11118010049 by Pennsylvania educators for local classroom Page use. 4 This permission does not extend to the 11 duplication of materials for commercial use.