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# Mensuration

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### Mensuration

1. 1. MENSURATION<br />
2. 2. DEFINITION OF MENSURATION<br />Topic dealing with the use of formulae to calculate Perimeters, Areas and Volumes of plain shapes and solid ones (prisms).<br />
3. 3. PERIMETER AND AREA<br />PERIMETER<br />THE PERIMETER IS THE DISTANCE AROUND THE BOUNDARY OF A PLANE CLOSED FIGURE.<br />AREA<br />AREA CAN BE DEFINED AS THE SPACE COVERER BY THE SURFACE OF A FIGURE.<br />
4. 4. L<br />L<br />L<br />PERIMETER<br />THERE ARE DIFFERENT FORMULAES FOR FINDING THE PERIMETER OF A PLANE FIGURE:<br />SQUARE: 4 X s<br />RECTANGLE: 2 X (l + b) <br />CIRCLE:2 X 3.14 X r<br />
5. 5. AREA OF 2D FIGURES<br />THERE ARE DIFFERENT FORMULAES FOR FINDING THE AREA OF A PLANE FIGURE:<br />RECTANGLE: l X b <br />SQUARE: s2<br />TRIANGLE: ½ X b X h<br />PARALLELOGRAM: b X h <br />CIRCLE: 3.14 X r2 <br />TRAPEZIUM : ½ X h(a+b) (WHERE a IS FIRST PARALLEL LINE , b IS SECOND PARALLEL LINE AND h IS HEIGHT)<br />
6. 6. h<br />b<br />l<br />AREA OF 3D FIGURES<br />THERE ARE DIFFERENT FORMULAES FOR FINDING THE AREA OF A PLANE FIGURE:<br />CUBE:6l2<br />CUBOID:2 X h X (l + b)<br />CYLINDER: 2 X 3.14 X r X (r +h)<br />
7. 7. 1000m<br />BASIC PROBLEMS<br />Q1. SHYAM HAS A SQUARE PLOT OF SIDE 1000m.<br /> FIND THE AREA.<br /> ANS1. SIDE OF SQUARE PLOT = 1000M<br /> THEREFORE, AREA = 1000m2 = 10,00,000m2<br />
8. 8. 300km<br />200km<br />120km<br />BASIC PROBLEMS<br />Q2. 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.<br />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<br />
9. 9. 5m<br />500M<br />400M<br />5m<br />BASIC PROBLEMS<br />Q3 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.<br />ANS3 LENGTH OF RECTANGLE = 500m BREADTH OF RECTANGLE = 400m <br />THE AREA OF RECTANGLE = 500m X 400m<br /> =2,00,000m2<br />LENGTH OF OUTER RECTANGLE = 510m<br />BREADTH OF OUTER RECTANGLE = 410m<br />AREA OF OUTER RECTANGLE <br />= 510m X 410m = 2,09,100m2<br />AREA OF FOOTPATH = 2,09,100m2 –2,00,000m2<br /> = 9100m2<br />
10. 10. CREDITS<br />PUILKIT<br />VIII-D<br />