Math Quiz -Geometry Report a question What's wrong with this question? You cannot submit an empty report. Please add some details. Math Quiz -Geometry Covering: geometric concepts such as lines, angles, triangles, quadrilaterals, circles, and various coordinate geometry topics, including the distance formula, midpoint formula, and slope. 1 / 5 1. A circle has a diameter of length 18. What is the area of the circle? a) 63π b) 81π c) 99π d) 81π/2 To find the area of a circle with a given diameter, we first need to find the radius by dividing the diameter by 2: radius = diameter / 2 radius = 18 / 2 radius = 9 Now, we can use the formula for the area of a circle: Area = πr² Substitute r = 9 into the formula: Area = π(9²) Area = 81π So, the area of the circle is 81π. The correct answer is B) 81π. 2 / 5 2. In triangle PQR, angle P is 30 degrees, angle Q is 60 degrees, and side PQ has a length of 10. What is the length of side QR? a) 5√3 b) 10√3 c) 15√3 d) 20√3 Using the Law of Sines in triangle PQR, we have: sin(P) / PQ = sin(Q) / QR Given the angle P is 30 degrees, angle Q is 60 degrees, and side PQ has a length of 10, we can substitute the values into the formula: sin(30) / 10 = sin(60) / QR Simplifying: 1/2 / 10 = √3/2 / QR Now, we can cross-multiply to solve for QR: QR = (10 * √3/2) / (1/2) QR = 10√3 So, the length of side QR is 10√3. The correct answer is B) 10√3. 3 / 5 3. The midpoint between two points A(1, 6) and B(7, 4) is M. What are the coordinates of M? a) (3, 5) b) (4, 5) c) (5, 5) d) (4, 6) To find the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂), we can use the formula: (midpoint_x, midpoint_y) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2) Given the endpoints A(1, 6) and B(7, 4), we have: midpoint_x = (1 + 7) / 2 = 8 / 2 = 4 midpoint_y = (6 + 4) / 2 = 10 / 2 = 5 The coordinates of the midpoint M are (4, 5). The correct answer is B) (4, 5). 4 / 5 4. What is the circumference of a circle with a radius of 6? a) 6π b) 9π c) 12π d) 18π The circumference of a circle with radius r is given by the formula: C = 2πr Given that the circle has a radius of 6, we can substitute r = 6 into the formula: C = 2π(6) = 12π So, the circumference of the circle is 12π. The correct answer is C) 12π. 5 / 5 5. What is the sum of the interior angles of a hexagon? a) 360° b) 540° c) 620° d) 720° The sum of the interior angles of a polygon can be found using the formula: sum = (n - 2) × 180° where n is the number of sides of the polygon. For a hexagon, the number of sides is 6: sum = (6 - 2) × 180° sum = 4 × 180° sum = 720° So, the sum of the interior angles of a hexagon is 720°. The correct answer is D) 720°. Your score is 0% Restart Quiz