Maths-
General
Easy

Question

Find the area of a quadrilateral whose sides are 9 cm, 40 cm, 28cm and 15 cm and the angle between the first two sides is a right angle

hintHint:

Using pythagoras theorem, find the length of  side AC.
area of quadrilateral ABCD = area of Δ ABC + area of Δ ADC
Find area of area of Δ ADC by heron's formula for finding the area of triangle

The correct answer is: 306 m2


    Ans :- 306 (in sq.centimeters)
    Explanation :-
    Step1 :- Find the length of side Ac using pythagoras theorem,
    In Δ ABC , AC2 = AB2 + BC2
    We know that AB = 9 and BC = 40
    Substituting the values we get  AC2 = 92 + 402 = 81+1600 = 1681 =412
    We get AC =  41 cm

    Step2:- Find the area of Δ ABC,
    Here,Δ ABC is a right angle triangle .
    Area of right angle triangle = ½ (product of lengths of  perpendicular sides)
    Area of Δ ABC = ½ (40 × 9)
    Area of Δ ABC = 180 cm2
     
    Step 3:- Find the area of Δ ADC from heron's formula
    Here, side length of triangle are 15,28 and 41 cm
    Heron's formula for area of triangle with side length
    a,b,c are Area equals 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 3 end fraction
    Let a = 28 ;b = 15 ;c = 41   We get sequals fraction numerator 28 plus 15 plus 41 over denominator 2 end fraction equals42
    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
    square root of 42 cross times 14 cross times 27 cross times 1 end root
    = square root of 15876 equals 126 cm squared                                                                       

    We get area of Δ ADC = 126 (cm2)

    Step 4:- Find the area of the Patch
    area of patch ABCD = area of Δ ABC + area of Δ ADC
    = 180 cm2 + 126 cm2
    = 306  cm2
    Therefore area of patch ABCD = 306  cm2.

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