Odpowiedź:
b = 10 [j]
c = 8 [j]
a - dłuższa podstawa = ?
h - wysokość trapezu = ?
h/c = sin30°
h = c * sin30° = c * 1/2 = 8 * 1/2 = 4 [j]
(a - b)/2 : c = cos30° = √3/2
(a - b)/2 = c * √3/2 = 8 * √3/2 = 4√3 [j]
a - b = 2 * 4√3 = 8√3
a = 8√3 + b = 8√3 + 8 = 8(√3 + 1) [j]
o - obwód trapezu = a + b + 2 * c = 8√3 + 8 + 10 + 2 * 8 =
= 8√3 + 8 + 10 + 16 = 8√3 + 34 = 2(4√3 + 17) [j]
P = pole trapezu = 1/2 * (a + b) * h = 1/2 * (8√3 + 8 + 10) * 4 =
= 2(8√3 + 18) = 2 * 2(4√3 + 9) = 4(4√3 + 9) [j²]
[j] - znaczy właściwa jednostka
