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"Question 3 Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.
Class 8 Mensuration Page 178"
Answered by admin @
Mensuration:
Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.
Plane Figure: A figure which lies in a plane is called a plane figure.
For e.g: a rectangle, square, a rhombus, a parallelogram, a trapezium.
Perimeter:
The perimeter of a closed plane figure is the total length of its boundary.
In case of a triangle or a polygon the perimeter is the sum of the length of its sides.
Unit of perimeter is a centimetre (cm), metre(m) kilometre(km) e.t.c
Area: The area of the plane figure is the measure of the surface enclose by its boundary.
The area of a triangle are a polygon is the measure of the surface enclosed by its sides.
A square centimetre (cm²) is generally taken at the standard unit of an area. We use square metre (m²) also for the units of area.
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Solution;
Given:
Length of the fence of a trapezium ABCD =120
m. BC = 48 m, CD = 17 m and AD = 40 m,
Length of the
fence of a trapezium ABCD =AB +BC+ CD+ AD
120=AB +
48+17+40
120 = AB + 105
120 – 105 = AB
AB= 15 m
Height (AB) = 15
m
Area of
Trapezium
= 1/2 x sum of parallel sides x perpendicular
distance
Area of Trapezium
= (1/2) (48+40) 15
= ½(88)(15)
= 44× 15
=660 m²
Hence, the area
of the field = 660 m²
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