The area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b 2.
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1 ALGEBRA Find each missing length. 21. A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of 64 square meters. What is the length of the other base? The area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b HONORS Estella has been asked to join an honor society at school. Before the first meeting, new members are asked to sand and stain the front side of a piece of wood in the shape of an isosceles trapezoid. What is the surface area that Allison will need to sand and stain? The required area is the difference between the larger trapezoid and the smaller trapezoid. The area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b 2. esolutions Manual - Powered by Cognero Page 1
2 For each figure, provide a justification showing that. 23. Set the area of the kite equal to the sum of the areas of the two triangles with bases d 1 and d 2. esolutions Manual - Powered by Cognero Page 2
3 24. Set the area of the kite equal to the sum of the areas of the two triangles with bases d 1 and d 2. ZWX = ZYX by SSS 25. CRAFTS Ashanti is in a kite competition. The yellow, red, orange, green, and blue pieces of her kite design shown are all congruent rhombi. a. How much fabric of each color does she need to buy? b. Competition rules require that the total area of each kite be no greater than 200 square inches. Does Ashanti s kite meet this requirement? Explain. The area of the yellow rhombus is or 24 in 2. Since the yellow, red, orange, green, and blue pieces area all congruent rhombi, each have an area of 24 in 2. The area of the purple kite-shaped piece is or 20 in 2. The total area of the entire kite is 24(5) + 20 or 140 in 2, which is less than the maximum 200 in 2 allowed. Therefore, her kite meets this requirement. esolutions Manual - Powered by Cognero Page 3
4 CCSS SENSE-MAKING Find the area of each quadrilateral with the given vertices. 26. A( 8, 6), B( 5, 8), C( 2, 6), and D( 5, 0) Graph the quadrilateral. The quadrilateral is a kite. The area A of a kite is one half the product of the lengths of its diagonals, d 1 and d 2. The lengths of the diagonals are 6 units and 8 units. Therefore, the area of the kite is 27. W(3, 0), X(0, 3), Y( 3, 0), and Z(0, 3) Graph the quadrilateral. The quadrilateral is a rhombus. The area A of a rhombus is one half the product of the lengths of its diagonals, d 1 and d 2. The lengths of the diagonals are 6 units each. Therefore, the area of the kite is esolutions Manual - Powered by Cognero Page 4
5 28. METALS When magnified in very powerful microscopes, some metals are composed of grains that have various polygonal shapes. a. What is the area of figure 1 if the grain has a height of 4 microns and bases with lengths of 5 and 6 microns? b. If figure 2 has perpendicular diagonal lengths of 3.8 microns and 4.9 microns, what is the area of the grain? a. Figure 1 is a trapezoid. The area of figure 1 is 22 square microns. b. Figure 2 is a rhombus. The area of figure 2 is about 9.3 square microns. esolutions Manual - Powered by Cognero Page 5
6 29. PROOF The figure at the right is a trapezoid that consists of two congruent right triangles and an isosceles triangle. In 1876, James A. Garfield, the 20th president of the United States, discovered a proof of the Pythagorean Theorem using this diagram. Prove that. Following is an algebraic proof. The trapezoid is on its side, so the bases are x and y and the height is x + y. Set the area of the trapezoid equal to the sum of the areas of the triangles and simplify. esolutions Manual - Powered by Cognero Page 6
7 DIMENSIONAL ANALYSIS Find the perimeter and area of each figure in feet. Round to the nearest tenth, if necessary. 30. Both diagonals are perpendicular bisectors, so the figure is a rhombus and all four triangles are congruent. All of the sides are 12 feet, so the perimeter is 48 feet. Use trigonometry to find the lengths of the diagonals. Now find the area. esolutions Manual - Powered by Cognero Page 7
8 31. Use the triangle to find the dimensions of the isosceles trapezoid. The base of the triangle is 0.5(12 8) = 2. Don't forget to use dimensional analysis to convert the units to feet. 32. The figure is a kite because one of the diagonals is a perpendicular bisector. Find the perimeter. Convert the units to feet. esolutions Manual - Powered by Cognero Page 8
9 Use the triangle to find the lengths of the congruent parts of the diagonals. d 1 = = 6 Use the Pythagorean theorem to find the other piece of d 2. Now find the area of the kite. esolutions Manual - Powered by Cognero Page 9
10 COORDINATE GEOMETRY Find the area of each figure. 43. JKL with J( 4, 3), K( 9, 1), and L( 4, 4) Plot the points and draw the triangle. The length of base JL is 7 units. The corresponding height is from the line x = 9 to x = 4, so the height is 5 units. esolutions Manual - Powered by Cognero Page 10
11 44. RSTV with R( 5, 7), S(2, 7), T(0, 2), and V( 7, 2) Plot the points. The parallelogram has base length of 7 units. The height is from y = 2 to y = 7, so the height is 5 units. The area of the parallelogram is 7(5) or 35 units WEATHER Meteorologists track severe storms using Doppler radar. A polar grid is used to measure distances as the storms progress. If the center of the radar screen is the origin and each ring is 10 miles farther from the center, what is the equation of the fourth ring? Refer to the image on Page 780. The standard form of the equation of a circle with center at (h, k) and radius r is (x h) 2 + (y k) 2 = r 2. (h, k) = (0, 0) The fourth ring will be 40 miles away from the origin, so r = 40. Therefore, the equation is (x 0) 2 + (y 0) 2 = 40 2 or x 2 + y 2 = esolutions Manual - Powered by Cognero Page 11
12 Find x and y. 46. This is a triangle. Side opposite the 30 = a Side opposite the 60 = Hypotenuse = 2a For this triangle: Side opposite the 30 = 8 Side opposite the 60 = Hypotenuse = 16 Therefore, x = and y = This is a triangle. Side opposite the 30 = a Side opposite the 60 = Hypotenuse = 2a For this triangle: Side opposite the 30 = 9 Side opposite the 60 = Hypotenuse = 18 Therefore, x = 9 and y = esolutions Manual - Powered by Cognero Page 12
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1.1.1: Chapter 1 1-3. Shapes (a), (c), (d), and (e) are rectangles. 1-4. a: 40 b: 6 c: 7 d: 59 1-5. a: y = x + 3 b: y =!x 2 c: y = x 2 + 3 d: y = 3x! 1 1-6. a: 22a + 28 b:!23x! 17 c: x 2 + 5x d: x 2 +
AREA See the Math Notes box in Lesson for more information about area.
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GRADE LEVEL: FOURTH GRADE SUBJECT: MATH DATE: Read (in standard form) whole numbers. whole numbers Equivalent Whole Numbers
CRAWFORDSVILLE COMMUNITY SCHOOL CORPORATION 1 GRADE LEVEL: FOURTH GRADE SUBJECT: MATH DATE: 2019 2020 GRADING PERIOD: QUARTER 1 MASTER COPY 1 20 19 NUMBER SENSE Whole Numbers 4.NS.1: Read and write whole
ISBN Copyright 2015 The Continental Press, Inc.
Table of COntents Introduction 3 Format of Books 4 Suggestions for Use 7 Annotated Answer Key and Extension Activities 9 Reproducible Tool Set 175 ISBN 978-0-8454-8768-6 Copyright 2015 The Continental
3. Given the similarity transformation shown below; identify the composition:
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is formed where the diameters intersect? Label the center.
E 26 Get Into Shape Hints or notes: A circle will be folded into a variety of geometric shapes. This activity provides the opportunity to assess the concepts, vocabulary and knowledge of relationships
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Standard 4.G.1 4.G.2 5.G.3 5.G.4 4.MD.5
Draw and identify lines and angles, as well as classify shapes by properties of their lines and angles (Standards 4.G.1 3). Standard 4.G.1 Draw points, lines, line segments, rays, angles (right, acute,