Mensuration
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This document defines mensuration and provides formulas for calculating the perimeters and areas of various 2D and 3D shapes. It explains that mensuration deals with using formulas to calculate perimeters, areas, and volumes of plain and solid geometric figures. Formulas are provided for calculating the perimeters and areas of squares, rectangles, circles, triangles, parallelograms, trapezoids, cubes, cuboids, and cylinders. Some example problems are worked through applying these formulas to find perimeters and areas.
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Mensuration
- 1. MENSURATION
- 2. DEFINITION OF MENSURATIONTopic dealing with the use of formulae to calculate Perimeters, Areas and Volumes of plain shapes and solid ones (prisms).
- 3. PERIMETER AND AREAPERIMETERTHE PERIMETER IS THE DISTANCE AROUND THE BOUNDARY OF A PLANE CLOSED FIGURE.AREAAREA CAN BE DEFINED AS THE SPACE COVERER BY THE SURFACE OF A FIGURE.
- 4. LLLPERIMETERTHERE ARE DIFFERENT FORMULAES FOR FINDING THE PERIMETER OF A PLANE FIGURE:SQUARE: 4 X sRECTANGLE: 2 X (l + b) CIRCLE:2 X 3.14 X r
- 5. AREA OF 2D FIGURESTHERE ARE DIFFERENT FORMULAES FOR FINDING THE AREA OF A PLANE FIGURE:RECTANGLE: l X b SQUARE: s2TRIANGLE: ½ X b X hPARALLELOGRAM: b X h CIRCLE: 3.14 X r2 TRAPEZIUM : ½ X h(a+b) (WHERE a IS FIRST PARALLEL LINE , b IS SECOND PARALLEL LINE AND h IS HEIGHT)
- 6. hblAREA OF 3D FIGURESTHERE ARE DIFFERENT FORMULAES FOR FINDING THE AREA OF A PLANE FIGURE:CUBE:6l2CUBOID:2 X h X (l + b)CYLINDER: 2 X 3.14 X r X (r +h)
- 7. 1000mBASIC PROBLEMSQ1. SHYAM HAS A SQUARE PLOT OF SIDE 1000m. FIND THE AREA. ANS1. SIDE OF SQUARE PLOT = 1000M THEREFORE, AREA = 1000m2 = 10,00,000m2
- 8. 300km200km120kmBASIC PROBLEMSQ2. SHRI OWNS A TRAPEZIUM PLOT OF 1ST PARALLEL LINE = 300km , 2ND PARALLEL LINE = 200km AND THE DISTANCE BETWEEN THEM = 120km. FIND THE AREA OF THE PLOT.ANS2. 1ST PARALLEL LINE = 300km.THE 2ND PARALLEL LINE =200km AND HEIGHT = 120km. AREA = ½ x 120km (300km + 200km) . THEREFORE, AREA =½ X 120km X 500km = 30,000km2
- 9. 5m500M400M5mBASIC PROBLEMSQ3 RAM OWNS A RECTANGULAR PARK OF l = 500m AND b = 400m. HE CONSTRUCTS A FOOTPATH OF 5m ALONG ITS ALL SIDES. FIND THE AREA OF THE FOOTPATH.ANS3 LENGTH OF RECTANGLE = 500m BREADTH OF RECTANGLE = 400m THE AREA OF RECTANGLE = 500m X 400m =2,00,000m2LENGTH OF OUTER RECTANGLE = 510mBREADTH OF OUTER RECTANGLE = 410mAREA OF OUTER RECTANGLE = 510m X 410m = 2,09,100m2AREA OF FOOTPATH = 2,09,100m2 –2,00,000m2 = 9100m2