Formula lui Héron :
A=rad[p(p-a)(p-b)(p-c)]
p=semiperimetru=(17+10+21)/2=24
A=rad[24•(24-17)(24-10)(24-21)
A=rad[24•7•14•3]
A=rad[2^3 • 3 • 7 • 2 • 7 • 3]
A=rad[2^4 • 3^2 • 7^2]
A=2^2 • 3 • 7
A=84 cm^2
Răspuns:
Explicație pas cu pas:
P = 17 + 10 + 21 = 48
p = P : 2 = 48 : 2 = 24
Aria = √p(p-a)(p-b)(p-c) = √24(24-17)(24-10)(24-21) = √24*7*14*3
24*7*14*3 = 8*3*7*2*7*3 = 16*3^2*7^2 = 2^4*3^2*7^2 = (2^2*3*7)^2 = 84^2
Aria = √84^2 = 84
