Question

find the area of triangular board of
sides are 5cm,12cm and 13cm.

Answer 1

Given,
1st side = 5 cm (Let, a)
2nd side = 12 cm (Let, b)
3rd side = 13 cm (Let, c)
Now,
By Heron's formula:-
Ar.(∆)=√{s(s-a)(s-b)(s-c)}
Now,
s = (a+b+c)/2 = (5+12+13)/2
= 30/2 = 15
Now,
Ar.(∆) = √{15(15-5)(15-12)(15-13)}
= √{15*10*3*2}
= √{900}
= 30 cm²

Hope this helps you!

Answer 2

$semi \: perimeter = \frac{perimeter}{2}$

$perimeter = a + b + c \\ a = 5cm \\ b = 12cm \\ c = 13cm$

$semi \: perimeter \: = \frac{a + b + c}{2} \\ = \frac{5 + 12 + 13}{2 } \\ = \frac{30}{2} \\ = 15$

$area = \sqrt{s(s - a)( s- b)(s - c)} \\ = \sqrt{15(15 - 5)(15 - 12)(15 - 13)} \\ = \sqrt{15(15 - 5)(15 - 12)(15 - 13)} \\ = \sqrt{15(10)(3)(2)} \\ = \sqrt{15(60)} \\ = \sqrt{900} \\ = 30$

→→→ Slide to see the remaining part of the sum

I hope this helps you

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