Area and volume of plane figures, Formulae, math Assignment Help

Area and volume of plane figures - Area and volume of plane figures, Formulae, math


(1)     Regular polygon: Let each side of a regular polygon of n sides be a.

(i)      Each angle of the polygon

(ii)     Area of the polygon = n × (area of an isosceles t. with base a and height82_th2.jpg  tan82_th2.jpg ), where q is the interior angle of the polygon.


           sq. units.

(2)     Area and perimeter: Triangle:

(i)      Area =  × 1/2 *Base × Height

(ii)     Area =2480_th3.jpg

where 2s = a + b + c

(iii)    Perimeter = a + b + c.

(3)     Area and perimeter: Right- angled isosceles triangle: Let equal sides of right angled isosceles triangle

          (i)      Height =  1928_th4.jpg

(ii)     Area =  266_th5.jpg

          (iii)    Perimeter = (2a + 1828_th6.jpg a)

(4)     Area and perimeter: Equilateral triangle: Let each side = a, then, we have:

(i)      Height =  1477_th7.jpg

(ii)     Area2153_th8.jpg

(iii)    Perimeter = 3a

(5)     Area of Quadrilateral

1/2*AC × (h1 + h2) 

(6)     Area and perimeter: Rectangle:

          (i)      Area = l × b

(ii)     Length =669_th9.jpg

Breadth =Area/lemgth

(iii)    Perimeter = 2 ( l + b)

(iv)    Diagonal =1627_root4.jpg

Area of 4 walls = Perimeter × height


= 2 ( l + b) × h, where h is the height.


(7)     Area and perimeter: Square:

Let each side of square be a, then, we have:

Area = (side)2 = a2

Area = 1/2* (diagonal)2

Side =  71_th12.jpg


Perimeter = 4a


Diagonal =  1487_th13.jpg


(8)     Area and perimeter: Parallelogram:

(i)      Area = Base × Height

(ii)     Perimeter = 2 (Sum of adjacent sides).

(9)     Rhombus: Rhombus is a parallelogram all of whose sides are equal. Its diagonals bisect each other at right angles. Let d1 d2 be the diagonals of a rhombus, we have


(i)      Area = 1/2* d1d2


(ii)     Side =1204_th14.jpg

(iii)    Perimeter = 4 × side


(10)   Trapezium: Trapezium is a quadrilateral, two of whose sides are parallel. A trapezium whose non parallel sides are equal is known as an isosceles trapezium.

Area of trapezium


= 1/2* (Sum of parallel sides) × Distance between them

=  1/2*(a + b) × d


The word 'Mensuration' is derived from the Greek word 'Mensuration' meaning 'to measure' and refers to that branch of mathematics and deals with the measurement of geometric magnitudes, such as areas of surfaces and volumes of solids. It is a practical branch of mathematics.

Mensuration is divided into two parts:

(i)      Plane mensuration deals with the measurement of solids, perimeters and areas of plane figures like triangle, polygons, etc.

(ii)     Solid mensuration deals with the measurement of surfaces, areas and volumes of solid figures like cube, cuboid, sphere, cone, cylinder etc. 


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