SAT Geometry Mastering Geometry: SAT Geometry Quiz - part 1The quiz consists of 200 questions, and the user will be presented with a unique set of 10 questions in each session for a diverse experiencePlease note that answers cannot be deselected once chosen in the quiz, so make your choices carefully for an optimal testing experience.Each question is meticulously crafted to mirror the complexity and diversity of geometric problem-solving you'll encounter in the SAT.Use it as a targeted practice tool to identify and address specific areas of improvement.Track your progress and see your geometric proficiency grow. 1. In the figure above, the sum of the areas of the three shaded semicircles with centers at A, B, and C is X, and the area of the larger semicircle below the line is Y. If Y − X = kπ, what is the value of k? 1 4 3 2 None 2. In the figure above, if the area of square ABCD is 64, what is the areaof equilateral triangle BEC? 8√3 8 16√3 12√3 None 3. Katie hikes 5 miles north, 7 miles east, and then 3 miles north again.What number of miles, measured in a straight line, is Katie from herstarting point? √113 10 √83 13 None 4. In the figure above, OA⊥AB, and m∠BOC = 45°. If the coordinates ofpoint A are (0, 3) and the coordinates of point C are (7, 0), what is thenumber of square units in the area of quadrilateral OABC? 30 25 20 15 None 5. In the figure above, what is y in terms of x? x 3/4 x 4/3 x 3/2 x None 6. In the figure above, if the radius length of circle O is 10, OY⊥AB, andAB = 16, what is the length of segment XY? 4 6 3 2 None 7. If one pair of opposite sides of a square are increased in length by 20%and the other pair of sides are increased in length by 50%, by whatpercent is the area of the rectangle that results greater than the area ofthe original square? 75% 80% 70% 77% None 8. In the figure above, PA is tangent to circle O at point A, PB is tangentto circle O at point B. Angle AOB measures 120° and OP = 24/π What isthe length of minor arc AB? 5 8 4 6 None 9. In △RST above, what is the value of x?Write your answer in numbers only %BLANK% 100 None 10. The diagram above shows a semicircular arch over a street that has a radius of 14 feet. A banner is attached to the arch at points A and B, such that AE = EB = 5 feet. How many feet above the ground are these points of attachment for the banner, correct to the nearest tenth of a foot? 16.1 14.1 13.1 15.1 None 11. The circle shown above has center O and a radius length of 12. If P isthe midpoint of OA and AB is tangent to circle O at B, what is the areaof the shaded region? 128π 96π 81π 120π None 12. In the figure above, OACB is a square with area 4x². If OA and OB areradii of a sector of a circle O, what is the perimeter, in terms of x, of theunbroken figure? x(4 + 3π) x(6 + 4π) 4(x + 2π) x(3 + 4π) None 13. Kristine is riding in car 4 of the Ferris wheel represented in the diagram above, which is 84/π meters from car 8. The Ferris wheel is rotating in the direction indicated by the arrows. If each of the cars are equally spaced around the circular wheel, what is the best estimate of the number of meters in the distance through which Kristine’s car will travel to reach the bottom of the Ferris wheel before her car returns to the same position? 42.0 64.75 52.50 105.0 None 14. In the figure above, if line segment AB is parallel to line segment CD,what is the value of y?Write your answer in numbers only 15. In the figure above, what is the number of square units in the area of the shaded region? 12.5 13.5 11.5 14.5 None 16. Two hikers started at the same location. One traveled 2 miles east andthen 1 mile north. The other traveled 1 mile west and then 3 milessouth. At the end of their hikes, how many miles apart were the twohikers? 8 5 10 1 None 17. In the figure above, quadrilaterals ABED, BFGC, and ACHJ aresquares. If the area of equilateral ABC is 16 square inches, what isthe number of inches in the perimeter of polygon ADEBFGCHJA 72 82 62 92 None 18. If the coordinates of the endpoints of a diagonal of a square are (−2, −3) and (5, 4), what is the number of square units in the area of the square? 7 98 21 49 None 19. In the figure above, ACDEFG is a regular hexagon. Sides DC and GAare extended such that A is the midpoint of BG and C is the midpointof BD. If the area of △ABC is 9 square centimeters, what is thenumber of centimeters in the perimeter of polygon ABCDEFG? 1 42 45 0 None 20. In rectangle ABCD, point P divides BC such that BP is 25% of thelength of BC. If the area of quadrilateral ABPD is 3/4, what is the area ofrectangle ABCD? 15/6 6/5 9/8 3/2 None 21. Which of the following could be an equation of the circle above? (x − 4)²+ (y + 2)²= 17 (x + 4)²+ (y- 2)²= 17 (x + 4)²+ (y- 2)²= 13 (x − 4)²+ (y + 2)²= 13 None 22. In the figure above, the vertices of square ACEG are the centers of fourquarter circles of equal area. What is the best approximation for thearea of the shaded region? (Use π = 3.14.) 1.57 0.79 0.64 0.86 None 23. What is the number of square units in the area of the region in the firstquadrant of the xy-plane that is bounded by y = |x| + 2, the line x = 5,the positive x-axis, and the positive y-axis? 45/6 45/2 44/5 44/7 None 24. In rectangle ABCD above, arcs BP and CP are quarter circles withcenters at points A and D, respectively. If the area of each quarter circleis π, what is the area of the shaded region?4-π/2 8-π 4-π/2 8-2π 4-π None 25. x²+ y²− 6x + 8y = 56What is the area of a circle whose equation is given above? 25π 6,561π 81π 162π None 26. In the figure above, each arc is a semicircle. If S is the midpoint of PQ and Q is the midpoint of PR, what is the ratio of the area of semicircle PS to the area of semicircle PR? 1/12 1/8 1/16 1/9 None 27. In the figure above, what is the value of x?Write your answer in numbers only 28. In the figure above, OABC is a square and B is a point on the circlewith center O. If AB = 6, what is the area of the shaded region? 9(π − 2) 9(π − 1) 18(π − 2) 12(π − 2) None 29. How many different triangles are there for which the lengths of thesides are 3, 8, and n, where n is an integer and 3 < n < 8? Five Four Three Two None 30. What is the number of sides of a polygon in which the sum of thedegree measures of the interior angles is 4 times the sum of the degreemeasures of the exterior angles? 14 10 12 No such polygon exists. 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