Mensuration is defined as the branch of mathematics dealing with the study of geometric shapes, their area and volume along with other related concepts. Basically, it’s all about measurement.
It uses algebraic equations and the geometric calculations for providing the measurement data regarding the depth, width, and the volume of a given object or the group of objects. The calculations of mensuration are considered very accurate despite the fact that the results obtained through mensuration are only estimates and not actual physical measurements.
There are two varieties of geometric shapes: 2D and 3D. The 2D shapes include a square, rectangle, rhombus, parallelogram, triangle, trapezoid and circle meanwhile the 3D shapes include cube, cuboids, cylinder, cone, prism, pyramid, sphere and hemisphere.
Perimeter is the distance around the boundary and the area is the region that is covered by the closed plane figure. Volume is the amount of space that is occupied by a three dimensional object. Example, volume of an eraser is lesser than the volume of the box that contains it. Similarly, volume of the cupboard is lesser than the volume of the room occupying it.
The surface area of the solid is defined as the sum of the area of its faces.
IMPORTANCE OF USING MENSURATION IN DAILY LIFE
- While cooking, we measure the quantities according to their volume stated in the recipe books. Tools like spoons, measuring jugs are used to determine the volume.
- Even while baking a cake, we choose an appropriate mould with a specific width and length while understanding the area of the cake. We also check out the weight of the dry ingredients before adding them to avoid miscalculation.
- We check weather forecast before leaving the house. The thermometers are used to check the temperature so as to decide what to wear.
- While taking on a road trip, we check out the map and calculate the shortest distance to reach our destination. We try and cut down the miles and take short cuts. The speed of travelling can be measured through mensuration along with the length of the distance travelled.
- When you enter Starbucks or any other coffee or drink shop, the size of cup you order, gives you that particular volume of liquid in that cup.
- By knowing the area of the walls, we can very easily determine how much wallpaper, paint etc would be needed to paint or cover the entire wall. Same with the flooring and carpeting, we need to know the area of the room for exact measurements.
SOME IMPORTANT FORMULAES FOR MENSURATION
- Area of a rectangle (A) = Length (l) x Breadth (b)
- Perimeter of a rectangle (P) = 2 x (length + breadth)
- Area of a square = length x length
- Perimeter of a square = 4 x length
- Area of a parallelogram = length x height
- Perimeter of a parallelogram = 2 x (length + breadth)
- Area of a triangle = ½ x base x height
- Volume of a cuboid= length x breadth height
- Volume of a cube = length x length x length
- Volume of a cylinder = Πr2 height
- Area of a parallelogram = base x height
- Area of a rhombus = breadth x height = ½ diagonal 1 x diagonal 2
- Area of a trapezium = ½ (sum of the parallel sides) x altitude
- Area of a quadrilateral = ½ x (diagonal x sum of the altitudes on diagonals)