Question

Sa sec afle aria unui trapez isoscel care are bazele de 10 cm si 24 cm ear latura laterala de 25cm​

Answer 1

Notăm trapezul ABCD, AB || CD, BC = AD.

Notăm: a = AB = 24,  b=BC = 25,  c = CD = 10, d=DA =25

Calculăm semiperimetrul:

$\it p=\dfrac{a+b+c+d}{2}=\dfrac{24+25+10+25}{2}=\dfrac{84}{2}=42\\ \\ Vom\ folosi\ formula:\\ \\ \mathcal{A}=\sqrt{(p-a)(p-b)(p-c)(p-d)}\\ \\ p-a=42-24=18\\ \\ p-b=42-25=17\\ \\ p-c=42-10=32\\ \\ p-d=42-25=17$

$\it \mathcal{A}=\sqrt{18\cdot17\cdot32\cdot17}=\sqrt{17^2\cdot9\cdot2\cdot32}=\sqrt{17^2\cdot9\cdot64}=17\cdot3\cdot8=\\ \\ =51\cdot8=408\ cm^2$