Q. 54.0( 5 Votes )

Calculate the area of the triangle shown.



Answer :

Let ABC be the required triangle.
Draw perpendicular from AS on BC.



Let AS = x cm.


In Δ BAS,


ABS + BAS + ASB = 180°
45° + BAS + 90° = 180°
BAS = 45°
Δ BAS is an isosceles triangle.


AS = BS = x cm


BC = BS + CS = 4 cm
x + CS = 4 cm
CS = (4–x) cm



In Δ CAS,


ACS + CAS + ASC = 180°
60° + CAS + 90° = 180°
CAS = 30°


We know that sides of any triangle of angles 30°, 60° and 90°
are in the ratio 1: √3: 2 .


CS :AS: AC = 1: √3: 2
(4-x) :x : AC = 1: √3 :2
(4 - x) : x = 1 : √3
√3(4 - x) = x
4√3 - x√3 = x
x(√3 + 1) = 4√3



Multiplying and Dividing by (√3 - 1)





x = 2(√3 - 1) cm


In Δ BAC,


Height = x = 2(√3 - 1) cm and Base = 4 cm




Area (Δ) = 4(√3 - 1) cm2 = 10.92 cm2


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RELATED QUESTIONS :

Calculate the area of the triangle shown.


Kerala Board Mathematics Part-1