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CASA Math Study Sheet Standard 11: Measurement and Geometry ο Terms to know: o Perimeter: The distance around a shape. o Area: The amount of space inside the boundary of a flat (2-dimensional) shape. o Surface Area: The total area of the surface of a 3-dimensional object. o Volume: The amount of space that a substance or object occupies. o Circumference: The boundary line around a circle and its distance. o Polygon: A plane figure with at least three straight sides and angles. o Complementary Angle: Two angles are complementary when they add up to 90 degrees (a right angle). o Supplementary Angle: Two angles that are supplementary add up to 180 degrees (a straight angle). o Vertical Angle: Angles opposite each other when two lines cross that are also equal. o Adjacent Angle: Two angles are adjacent when they have a common side and a common vertex (corner point) and donβt overlap. o Similarity: Figures that are the same shape, but not necessarily the same size. o Congruence: Segments or angles in similar shapes that correspond to one another. o Pythagorean Theorem: ππ2 + ππ 2 = ππ² ; a formula for a right triangle where the square of the hypotenuse is equal to the sum of the squares of the other two sides. Calculate the area of each figure 1. 2. Developed by KH 1 CASA Math Study Sheet Standard 11: Measurement and Geometry 3. Diameter = 16 meters, find the area 4. Radius = 6 cm, find the area Find the circumference of a circle. 1. Radius = 7 ft, find the circumference Developed by KH 2 CASA Math Study Sheet Standard 11: Measurement and Geometry 2. Diameter = 5 mi, find the circumference 3. Diameter = 2 cm, find the circumference Find the surface area of the figure. 1. Developed by KH 3 CASA Math Study Sheet Standard 11: Measurement and Geometry 2. 3. 4. 5. Developed by KH 4 CASA Math Study Sheet Standard 11: Measurement and Geometry Find the volume of the figures. 1. 2. 3. 4. Developed by KH 5 CASA Math Study Sheet Standard 11: Measurement and Geometry 5. 6. 7. 8. 9. Developed by KH 6 CASA Math Study Sheet Standard 11: Measurement and Geometry 10. Solve the following word problems by creating scale drawings. 1. Tammy drew a scale drawing of a house and its lot. In real life, the house's driveway is 22 feet long. It is 11 inches long in the drawing. What scale did Tammy use? 2. Lauren made a scale drawing of the elementary school. The scale of the drawing was 1 centimeter = 2 meters. In the drawing, the school yard is 24 centimeters wide. What is the width of the actual school yard? 3. Luther made a scale drawing of a house and its lot. The scale he used was 1 inch = 10 feet. The actual width of the deck is 30 feet. How wide is the deck in the drawing? Developed by KH 7 CASA Math Study Sheet Standard 11: Measurement and Geometry Determine whether the following figures similar. 1. 2. Developed by KH 8 CASA Math Study Sheet Standard 11: Measurement and Geometry 3. Given similar figures, find the unknown value. 1. βDEF is similar to βJKL, what is the value of a? Developed by KH 9 CASA Math Study Sheet Standard 11: Measurement and Geometry 2. βABC is similar to βDEF, what is the value of n? Answer the following questions regarding angles. 1. 2. Developed by KH 10 CASA Math Study Sheet Standard 11: Measurement and Geometry 3. 4. 5. 6. Developed by KH 11 CASA Math Study Sheet Standard 11: Measurement and Geometry Find measures of the unknown angles. 1. 2. 3. 4. The measure of an angle is 59°. What is the measure of a supplementary angle? Developed by KH 12 CASA Math Study Sheet Standard 11: Measurement and Geometry 5. The measure of an angle is 65°. What is the measure of a complementary angle? 6. Apply the Pythagorean Theorem to find missing lengths. 1. Developed by KH 13 CASA Math Study Sheet Standard 11: Measurement and Geometry 2. 3. 4. Developed by KH 14 CASA Math Study Sheet Standard 11: Measurement and Geometry Apply the Pythagorean Theorem to solve the word problem. 1. Millersburg Street and Lakewood Avenue intersect. If the diagonal distance across the intersection is 10 meters and Millersburg Street is 6 meters wide, how wide is Lakewood Avenue? 2. Clarksville is 8 kilometers due north of the airport, and Livingston is due east of the airport. If the distance between Clarksville and Livingston is 17 kilometers, how far is Livingston from the airport? 3. After school, Andy skateboards directly from school to a movie theater and then from the movie theater to a candy store. The movie theater is 12 kilometers south of the school and the candy store is 5 kilometers east of the movie theater. What is the straight-line distance between the school and the candy store? 4. A mouse has made holes in opposite corners of a rectangular kitchen. The width of the kitchen is 12 feet and the distance between the mouse's holes is 20 feet. What is the length of the kitchen? Developed by KH 15