Odpowiedź:
zad 1
H - wysokość graniastosłupa = 6,5 dm = 65 cm
a)
Pp - pole podstawy = 4 cm * 6 cm = 24 cm²
Pb - pole boczne = 2(8 + 4) cm * H = 2 * 12 cm * 65 cm =
= 24 cm * 65 cm = 1560 cm²
Pc - pole całkowite = 2 * Pp + Pb = 2 * 24 cm² + 1560 cm² =
48 cm² + 1560 cm² = 1608 cm²
b)
Pp = 1/2 * 3 cm * 5 cm = 1/2 * 15 cm² = 7,5 cm²
c - przeciwprostokątna podstawy = √(5² + 3²) cm = √(25 + 9) cm =
= √34 cm
Pb = (5 + 3 + √34) cm * H = (8 + √34) cm * 65 cm = 65(8 + √34) cm²
Pc = 2 * Pp + Pb = 2 * 7,5 cm² + 65(8 + √34) cm² =
= (15 + 520 + 65√34) cm² = (535 + 65√34) cm² = 5(107 + 15√34) cm²
c)
Pp - 1/2 * 8 cm * 6 cm = 1/2 * 48 cm² = 24 cm²
a - krawędź podstawy = √(4² + 3²) cm = √(16 + 9) cm = √25 = 5 cm
Pb = 4aH = 4 * 5 cm * 65 cm = 20 cm * 65 cm = 1300 cm²
Pc = 2 * Pp + Pb = 2 * 24 cm² + 1300 cm² = 48 cm² + 1300 cm² =
= 1348 cm²
d)
Pp = 1/2 * (10 + 4 ) dm * 8 dm = 1/2 * 14 dm * 8 dm = 7 dm * 8 dm = 56 dm²
c - ramię podstawy = √{8² + [(10 - 4)/2]²} dm = √(8² + 3²) dm =
= √(64 + 9) dm = √73 dm
Pb - pole boczne = (10 + 4 + 2√73) dm * 65 dm =
= (14 + 2√73) dm * 65 dm = 65 * 2(7 + √73) dm² = 130(7 + √73) dm²
Pc = 2 * Pp + Pb = 2 * 56 dm² + 130(7 + √73) dm² =
= 112 dm² + 130(7 + √73) dm² = (112 + 910 + 130√73) dm² =
= (1022 + 130√73) dm² =
zad 2
Pc - pole całkowite = 60 cm²
Pb - pole boczne = 48 cm²
Pc = 2 * Pp + Pb
Pc - Pb = 2Pp
Pp - pole podstawy = (Pc - Pb)/2 = (60 - 48) cm² : 2 = 12 cm² : 2 = 6 cm²
