Odpowiedź:
a) 9√2 cm
Obwód = 2p√2 = 2•(9√2)√2 = 2•9•2 = 36 cm
Pole = (1/2)p² = (1/2)(9√2)² = 81 cm²
b) √2/2 cm/
Obwód = 2√2/2)√2 = 2 cm
Pole = (1/2)(√2/2)² = 1/4 cm²
c) 1/2 cm
Obwód = 2p√2 = 2(1/2)√2 = √2 cm
Pole = (1/2)p² = (1/2)(1/2)² = 1/8 cm²
d) 3x
Obwód = 2p√2 = 2(3x)√2 = 6x√2
Pole P = (1/2)p²= (1/2)9x² = (9/2)x²
Szczegółowe wyjaśnienie:
5.
Przekątna kwadratu o boku a, z tw. Pitagorasa p = a√2 /:√2
to a = p/√2 = p√2 /√2√2 = p√2 /2 to a = p√2 /2
Obwód = 4a = 4p√2 /2 = 2p√2
Pole kwadratu obliczymy z połowy iloczynu przekątnych
Pole P = (1/2)p²
a) 9√2 cm
Obwód = 2p√2 = 2•(9√2)√2 = 2•9•2 = 36 cm
Pole = (1/2)p² = (1/2)(9√2)² = 81 cm²
b) √2/2 cm/
Obwód = 2√2/2)√2 = 2 cm
Pole = (1/2)(√2/2)² = 1/4 cm²
c) 1/2 cm
Obwód = 2p√2 = 2(1/2)√2 = √2 cm
Pole = (1/2)p² = (1/2)(1/2)² = 1/8 cm²
d) 3x
Obwód = 2p√2 = 2(3x)√2 = 6x√2
Pole P = (1/2)p²= (1/2)9x² = (9/2)x²
