This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the questions: 36. Find the area of the trapezium above Step 1: Identify the lengths of the parallel sides and the height from the diagram. The parallel sides are a = 7 cm and b = 13 cm. The perpendicular height is h = 8 cm. Step 2: Use the formula for the area of a trapezium, A = (1)/(2)(a+b)h. A = (1)/(2)(7 cm + 13 cm)(8 cm) Step 3: Calculate the area. A = (1)/(2)(20 cm)(8 cm) A = 10 cm × 8 cm A = 80 cm^2 The correct option is B. The area of the trapezium is B. 80 cm^2. 37. A circular arc subtends angle 150^ at the centre of a circle of radius 12 cm, calculate the area of the sector of the arc. Step 1: Identify the given values. Angle = 150^. Radius r = 12 cm. Step 2: Use the formula for the area of a sector, A = ()/(360^) r^2. A = (150^)/(360^) (12 cm)^2 Step 3: Calculate the area. A = (150)/(360) (144 cm^2) A = (5)/(12) (144 cm^2) A = 5 ((144)/(12)) cm^2 A = 5 (12) cm^2 A = 60 cm^2 The correct option is D. The area of the sector is D. 60 cm^2. 38. Calculate the volume of a cuboid of length 0.76 cm, breadth 2.6 cm and height 0.82 cm. Step 1: Identify the given dimensions. Length l = 0.76 cm. Breadth b = 2.6 cm. Height h = 0.82 cm. Step 2: Use the formula for the volume of a cuboid, V = l × b × h. V = 0.76 cm × 2.6 cm × 0.82 cm Step 3: Calculate the volume. V = 1.976 cm^2 × 0.82 cm V = 1.62032 cm^3 Rounding to two decimal places, V ≈ 1.62 cm^3. The correct option is A. The volume of the cuboid is A. 1.62 cm^3. 39. The locus of a point equidistant from the intersection of lines 3x - 7y + 7 = 0 and 4x - 6y + 1 = 0 is a Step 1: Understand the geometric interpretation of the problem. The intersection of two distinct lines is a single point. The locus of a point equidistant from a single fixed point is a circle, with the fixed point as its center. The correct option is C. The locus of a point equidistant from the intersection of lines 3x - 7y + 7 = 0 and 4x - 6y + 1 = 0 is a C. Circle. 40. The gradient of the straight line joining the points P (5, -7) and Q (-2, -3) is Step 1: Identify the coordinates of the two points. Point P: (x_1, y_1) = (5, -7). Point Q: (x_2, y_2) = (-2, -3). Step 2: Use the formula for the gradient (slope) of a line, m = (y_2 - y_1)/(x_2 - x_1). m = (-3 - (-7))/(-2 - 5) Step 3: Calculate the gradient. m = (-3 + 7)/(-7) m = (4)/(-7) m = -(4)/(7) The correct option is C. The gradient of the straight line joining the points P (5, -7) and Q (-2, -3) is C. -(4)/(7).