Mensuration Class 8 Notes

Mensuration deals with the measurement of area, perimeter, surface area and volume of different types of shapes.

Let us recall the area of all two-dimensional shapes.

Mensuration Class 8 – Area of Trapezium

By constructing EC || AB, we can split the given figure (AEDCBA) into two parts (Triangle ECD right-angled at C and Rectangle AECB), Here, b = a + c = 30 m

Now, Area of Triangle DCE:

1/2 × CD × EC= 1/2 × c × s

h = 1/2 ×10× 12 = 60 m²

Also, Area of rectangle AECB = AB × BC = h × a=12 × 20=240 m²

Therefore, Area of trapezium AEDB = Area of Triangle DCE + Area of rectangle AECB = 60 + 240 = 300 =300m²

Area of Trapezium = Height/2 (Sum of parallel sides) = 1/2 h(a+b)

Mensuration Class 8 – Area of General Quadrilateral

Diagonal AC divides the given quadrilateral into two triangles i.e. Triangle ABC and Triangle ADC.

Now, Area of Quadrilateral ABCD = Area of Triangle ABC + Area of Triangle ADC.

=1/2 × AC × h₁ + 1/2 × AC × h₂ =1/2 × d × (h₁ +h₂)

Where, d = The length of diagonal of a quadrilateral.

The area of other polygons (pentagon, hexagon, etc.) can be determined, by splitting them into a number of triangles and finding the respective areas.