Mensuration Areas Perimeters Class 10 Questions for BIHAR POLICE CONSTABLE

Rectangle and Square

A rectangle is a 4-sided shape with opposite sides equal and all angles 90 degrees. A square is a special rectangle where all four sides are equal. These are the most basic shapes tested. In Bihar Police exams, rectangle/square questions often involve finding missing dimensions or comparing areas.

• Rectangle: length and breadth can be different; square: all sides equal (side = s)
• Perimeter is the total distance around the shape—add all outer edges
• Area is the space inside—multiply length by width
• If perimeter is given, you can find one dimension if the other is known
• Watch units: if length is in metres, area will be in square metres

Circle

A circle is a round shape where all points are equidistant from the centre. The key measurements are radius (distance from centre to edge) and diameter (distance across through centre). Circles appear in 1-2 questions per paper in Bihar Police exams, often combined with other shapes.

• Radius (r) = half of diameter (d); so d = 2r
• Use π = 22/7 for most problems unless specified otherwise (π ≈ 3.14 for decimals)
• Area depends on radius squared—larger radius means much larger area
• Perimeter of a circle is called circumference
• Common mistake: confusing diameter with radius in formulas

Triangle

A triangle has 3 sides and 3 angles. For area calculation, you need the base and height (perpendicular distance from base to opposite vertex). The height must be perpendicular to the base—this is a common confusion point. Perimeter is simply the sum of all three sides.

• Base and height must be perpendicular to each other
• Height is not the same as the slant side—always measure vertically
• Perimeter = sum of all three sides (no formula needed, just add)
• For right-angled triangles, the two perpendicular sides can be base and height
• Equilateral triangle: all sides equal; isosceles: two sides equal

Trapezium (Trapezoid)

A trapezium is a 4-sided shape with one pair of parallel sides. The parallel sides are called bases. The perpendicular distance between the parallel sides is the height. Trapezium questions are less common but do appear in Bihar Police exams, especially in composite figure problems.

• Two parallel sides (bases) and two non-parallel sides
• Height is always perpendicular distance between the two parallel sides
• Area formula uses both parallel sides—average them first, then multiply by height
• Perimeter = sum of all four sides
• Often combined with rectangles or triangles in composite figure problems

Composite Figures and Practical Problems

Bihar Police exams often test real-world scenarios: a field shaped like a rectangle with a semicircular end, a room with a circular table, or a plot divided into sections. The strategy is to break the composite figure into standard shapes, calculate each area separately, then add or subtract as needed.

• Identify each simple shape within the composite figure
• Calculate area of each shape using standard formulas
• Add areas if shapes are combined; subtract if one is removed from another
• Always check units and convert if necessary (e.g., cm to m)
• Draw a rough sketch to visualize the problem—saves time and errors

• Confusing radius and diameter in circle formulas—always check which one the problem gives you. If diameter is given, divide by 2 first.
• Forgetting that height in triangle/trapezium must be perpendicular to the base. Slant height or side length is NOT the same as height.
• Using wrong value of π—some problems expect 22/7, others 3.14. Read carefully. If not specified, use 22/7 for cleaner answers.
• Mixing up area and perimeter—area is space inside (square units), perimeter is boundary length (linear units). They have different formulas.
• In composite figures, adding areas when you should subtract (or vice versa). Carefully read whether a shape is added to or removed from the main figure.

• AREA = SPACE INSIDE (square units); PERIMETER = BOUNDARY (linear units). Think: area fills a bucket, perimeter is the fence.
• For circles: 'Radius is half, diameter is whole.' r = d/2. Then use πr² for area, 2πr for circumference.
• For triangles: 'Half base times height'—the (1/2) factor is crucial. Forget it and your answer is double.
• TRAPEZIUM trick: 'Add the two bases, divide by 2, multiply by height.' (b1 + b2)/2 × h = average base × height.

• Bihar Police Constable papers typically have 1-2 straightforward area/perimeter questions and 1-2 slightly trickier composite figure or word-problem questions. Time allocation: 2-3 minutes per question.
• Recent papers show a preference for circle + rectangle combinations (e.g., 'A rectangular field with semicircular ends'). Practice these composite shapes.
• Always write the formula before substituting numbers. This reduces careless errors and shows your working if partial marks are awarded.
• Unit conversion is tested: a problem might give length in metres but ask for area in cm². Convert dimensions first, then apply formula.
• Diagram-based questions are increasing—if a figure is provided, label the dimensions clearly and mark perpendicular heights with a right-angle symbol.