pls tell the answer for this question
Answers
384cm^2(answer)
Step-by-step explanation:
we can find the third side/ hypotenuse of the triangle by pythagoras theorem so:-
a^2 + b^2 = c^2
let's take the third side or hypotenuse as x
(16)^2 + (12)^2 = x^2
256 + 144 = x^2
400 = x^2
√400 = X
20cm= X
ok so now we know all three sides... To find the area we can use the Heron's formula which is:-
area = √(s(s-a)(s-b)(s-c))
where s = (a+b+c)/2
a,b and c are the sides of the triangle
AREA OF THE BIG TRIANGLE:-
a=52cm
b=48cm
c=20cm
s= (52+48+20)/2 = 120/2 = 60
therefore, area of big triangle:-
√(60*(60-52)*(60-48)*(60-20))
√(60*(8)*(12)*(40))
(now we can divide these numbers in there factors to find out there square root)
√((2*3*5*2)*(2*2*2)*(2*3*2)*(2*2*5*2))
√(2*3*5*2*2*2*2*2*3*2*2*2*5*2)
√(2*2*2*2*2*2*2*2*2*2*3*3*5*5)
(now we can take the common factors out)
there are:-
ten 2= 5 pairs of 2
two 3= 1 pair of 3
two 5= 1 pair of 5
therefore:-
area of big triangle= 2*2*2*2*2*3*5
=> 480cm^2
AREA OF SMALL TRIANGLE
a=12cm
b=16cm
c=20cm
s= (12+16+20)/2= 48/2= 24
therefore, area of small triangle:-
√(24(24-12)(24-16)(24-20))
√(24*(12)*(8)*(4))
(now we can divide these numbers in there factors to find out there square root)
√((2*2*2*3)*(2*2*3)*(2*2*2)*(2*2))
√(2*2*2*3*2*2*3*2*2*2*2*2)
√(2*2*2*2*2*2*2*2*2*2*3*3)
(now we can take the common factors out)
there are:-
ten 2= 5 pairs of 2
two 3= 1 pair of 3
therefore:-
area of small triangle= 2*2*2*2*2*3
=>96cm^2
THE AREA OF SHADED PART:-
area of big triangle - area of small triangle
therfore,
the area of shaded part= 480-96
=> 384cm^2 ( answer )
I hope you understood the explanation.