z.1
Mamy trapez ABCD
AB =a , CD =b
CE =h
a+b = 8 cm , P=16 cm^2
P =[(a+b)/2]*h
16 = [8/2]*h
16 =4*h --> h = 16 : 4 = 4
h = 4cm
AC = x , x = (a+b)/2 = 8 :2 = 4
x= 4cm
c^2 =x^2 + h^2
c^2 = 4^2 + 4^2 =16 + 16 =16*2
c = pierwiastek kw. z (16*2) = 4*pierw. kw. z 2.
Odp. c= 4 pierw. kw. z 2
z.2
Przy tych samych oznaczeniach
AC =c = 10 cm
CE = h = 6 cm
AB =a, CD =b
AE =x
x^2 +h^2 =c^2
x^2 = 10^2 - 6^2 = 100 - 36 = 64
x= pierw. kw. z 64 = 8
AE = x = 8 cm.
Ale ( a+b )/2 = x
Stad P =[ (a+b)/2] * h =x*h =8*6 = 48
Odp. P = 48 cm^2
