mensuration
- Mensuration is the branch of mathematics that studies the measurement of the geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc.
- Here, the concepts of mensuration are explained and all the important mensuration formulas provided.
- A branch of mathematics that talks about the length, volume, or area of different geometric shapes is called Mensuration.
- These shapes exist in 2 dimensions or 3 dimensions.
what is mensuration
Here we can discuss about what is mensuration
- Mensuration is a topic in Geometry which is a branch of mathematics.
- Mensuration deals with length, area and volume of different kinds of shape- both 2D and 3D. So moving ahead in the introduction to Mensuration.
- 2D shape is a shape that is bounded by three or more straight lines or a closed circular line in a plane. These shapes have no depth or height. They have two dimensions length and breadth. Therefore called 2D figures or shapes. For 2D shapes, we measure Perimeter (P) and Area (A).
- 3D shape is a shape that is bounded by a number of surfaces or planes. These are also referred to as solid shapes. These shapes have height or depth unlike 2D shapes, they have three dimensions Length, Breadth and Height/Depth and therefore they are called 3D figures. 3D shapes are actually made up of a number of 2D shapes. Also, know as solid shapes, for 3D shapes we measure Volume (V), Curved Surface Area (CSA), Lateral Surface Area (LSA) and Total Surface Area (TSA).
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CLOSED FIGURE : the plain figure which have same starting and ending points is called closed figure.
OPEN FIGURE : the plain figure which have different starting and ending points is called open figure.
CONFEX FIGURE : the plain which have all angles than 180o then is called confex figure.
- In plain figure all diagnols lies inside the confex figure.
- if you take any two points in a figure the line segment joining those two points is also inside that figure then it is called confex figure.
CONCAVE FIGURE : at least one angle is greater than 1800 then the figure is called concave figure.
- if you take any two points in a figure the line segment joining those two points is also inside that figure then it is called confex figure.
- if you take any two points in the figure the line segment joining those two points is not belongs to interior of the diagram then it is called concave figure.
POLYGON : a closed and confex figure which has 3 or more sides is called polygon.
TRIANGLE : a closed , confex figure which has 3 sides is called triangle.
PERIMETER : total length of boundary line of the plain figure is called perimeter.
AREA : the amount of surface of enclosed plain figure is called area.
NOTE: the perimeter of a triangle is /AB+/BC+//CA = A+B+C
AREA OF RIGHT ANGLED TRIANGLE :
AREA EQUALITARAL TRIANGLE :
HERONS FORMULA :
AREA OF A RIGHT ANGLE ISOSCELES TRIANGLE :
QUADRILATERAL : a closed convex figure which has 4sides is called quadrilateral.
TRAPEZIUM : In a quadrilateral one pair of opposite sides are parallel.
PARALLELOGRAM : In a quadrilateral opposite sides are parallel the lengths of the diagonals are not equal is called parallelogram.
RECTANGLE : In a parallelogram one angle is 90 degrees then it is called rectangle.
RHOMBUS : In a quadrilateral all sides are equal but lengths of the diagonals are not equal then is called rhombus.
SQUARE : In a quadrilateral all sides equal and diagonals are also equal then it is called square. (or)
in a rhombus one angle is 90 degrees then it is called square.
- all squares are rectangles.
- all squares are rhombus.
- all squares are parallelograms.
- all squares are trapeziums.
- all squares are quadrilaterals.
- some rhombus are squares.
- some rhombus are rectangles.
- some rectangles are rhombus.
- some rectangles are squares.
- all rhombus are parallelogram.
- all rhombus are trapeziums.
- all rhombus are quadrilaterals.
- all rectangles are parallelograms.
- all rectangles are trapeziums.
- all rectangles are quadrilaterals.
- all parallelograms are trapeziums.
- all parallelograms are quadrilaterals.
- all trapeziums are quadrilaterals.
- some quadrilaterals are trapezium.
- some quadrilaterals are parallelograms.
- some quadrilaterals are rectangles.
- some quadrilaterals are rhombus.
- some quadrilaterals are squares.
- some trapeziums are parallelograms.
- some trapeziums are rectangles.
- some trapeziums are rhombus.
- some trapeziums are squares.
- some parallelograms are rectangles.
- some parallelograms are rhombus.
- some parallelograms are squares.
types of quadrilaterals | no of measurements we need for construction |
square | 1 |
rhombus | 2 |
rectangle | 3 |
parallelogram | 4 |
trapezium | 5 |
quadrilateral | 6 |
CIRCLE : The locus of the points which are equal distance from the fixed point is called a circle denoted by (o).
the fixed point is called centre of the circle.
RADIUS : The distance between the center of the circle and the point on the circle is called radius.
CHORD : A line segment joining any two points on a circle is called chord.
DIAMETER : The largest chord of the circle is called diameter.
NOTE : All diameters passes through the centre of the circle.
we can draw infinite diameter on the circle. it is denoted by (d).
ARC : The part of the circle is called arc.
SECTOR : The area between two radius OA,OB and ARC AB is called sector.
FORMULAS :
3-d figures : the plane figures which have 3 measures (length,breadth,height) is called 3-d figures.
eg: cube,cuboid,cylinder,cone,sphere,hemisphere