Maths-
General
Easy

Question

A field in the form of a parallelogram has sides 28 m and 15 m and one of the diagonal is 41 m. Find the area of the parallelogram.

hintHint:

area of parallelogram  ABCD = area of Δ ABC + area of Δ ADC
In parallelogram diagonal divide the area in to two equal parts
I. e  area of Δ ABC =  area of Δ ADC.
Find area of area of Δ ABC by heron's formula for finding the area of triangle

The correct answer is: 252 m2


    Ans :- 252  (in sq. meters)
    Explanation :-
    Step 1:- Find the area of Δ ABC from heron's formula

    Here, side length of triangle are 15,28 and 41 m
    Heron's formula for area of triangle with side length
    a, b ,c are Area = square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root
    Where sequals fraction numerator a plus b plus c over denominator 2 end fraction
    Let a = 28 ;b = 15 ;c = 41   We get s = fraction numerator 28 plus 15 plus 41 over denominator 2 end fraction= 42
    Area of  Δ ADC= square root of 42 left parenthesis 42 minus 28 right parenthesis left parenthesis 42 minus 15 right parenthesis left parenthesis 42 minus 41 right parenthesis end root
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals square root of 42 cross times 14 cross times 27 cross times 1 end root end cell row cell equals square root of 15876 equals 126 straight m squared end cell end table
    We get the area of Δ ABC = 126 (m2).
    Step 2:- Find the area of  Δ ADC.
    In parallelogram diagonal divide the area in to two equal parts
    area of Δ ABC =  area of Δ ADC
    area of Δ ADC = 126 (m2).
     
    Step 3:- Find the total area of parallelogram
    area of parallelogram  ABCD = area of Δ ABC + area of Δ ADC
    area of parallelogram  ABCD = 126 (m2)+ 126 (m2)
    ∴Area of parallelogram  ABCD = 252 (m2).

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