MENSURATION

WHAT IS MENSURATION IN MATHEMATICS?

• Mensuration IS A BRANCH OF MATHEMATICS THAT DEALS WITH THE MEASUREMENT OF AREAS AND VOLUMES OF VARIOUS

GEOMETRICAL FIGURES. FIGURES SUCH AS CUBES, CUBOIDS, CYLINDERS, CONES AND SPHERES HAVE VOLUME AND AREA.

MENSURATION DEALS WITH THE DEVELOPMENT OF FORMULAS TO MEASURE THEIR AREAS AND VOLUMES. 

AREA OF QUADRILATERALS AND POLYGONS

SURFACE AREA OF SOLIDSVOLUME OF SOLIDS

WHAT WE WILL LEARN ?

THE AMOUNT OF SPACE INSIDE THE BOUNDARY OF TWO DIMENSIONAL SHAPE

THE DISTANCE AROUND THE OUTSIDE OF TWO DIMENSIONAL SHAPE `

AREA

PERIMETER

FOR PERIMETER

ADD UP LENGTH

OF ALL SIDS

Square (regular quadrilateral): all four sides are of equal length (equilateral), and all four angles are right angles. An equivalent condition is that opposite sides are parallel (a square is a parallelogram), that the diagonals perpendicularly bisect each other, and are of equal length. A quadrilateral is a square if and only if it is both a rhombus and a rectangle (four equal sides and four equal angles).

SQUARE

RECTANGLE Rectangle: all four angles are right angles. An equivalent condition is that the

diagonals bisect each other and are equal in length. Rectangles include squares and oblongs. Informally: "a box or oblong" (including a square).

TRIANGLEA triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.

PARALLELOGRAMParallelogram: a quadrilateral with two pairs of parallel sides. Equivalent conditions are that opposite sides are of equal length; that opposite angles are equal; or that the diagonals bisect each other. Parallelograms include rhombi (including those rectangles we call squares) and rhomboids (including those rectangles we call oblongs). In other words, parallelograms include all rhombi and all rhomboids, and thus also include all rectangles.

TRAPEZIUM

In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid . The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides (if they are not parallel; otherwise there are two pairs of bases). A scalene trapezoid is a trapezoid with no sides of equal measure, in contrast to the special cases below.

RHOMBUS Rhombus or rhomb: all four sides are of equal length. An equivalent condition is

that the diagonals perpendicularly bisect each other. Informally: "a pushed-over square" (but strictly including a square, too).

VOLUME OF SOLIDS

CUBE

Volume of CUBE = LENGTH X LENGTH X LENGTH = X X = ³

LENGTHLENGTH

LENGTH

A Cube has 6 square faces. The length of each square face is equal.

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CUBOIDA cuboid also has 6 faces but NOT all

the faces are equal

LengthBreadth

Height

Volume of CUBOID = LENGTH X BREADTH X HEIGHT = X X l b h