Question

Calculati aria patrulaterului ABCD, stiind ca A(1,6),B(-3,2),C(1,-2)si D(5,2)

Answer 1

A(xA, yA); B(xb, yB)

AB=√[(xB-xA)²+(yB-yA)²)]

A(1,6),B(-3,2),C(1,-2)si D(5,2)

AB=√[(-3-1)²+(2-6)²)]= √32=4√2

BC=√[(1+3)²+(-2-2)²)]= √32=4√2

CD==√[(5-1)²+(2+2)²)]= √32=4√2

AD=√[(5-1)²+(2-6)²)]= √32=4√2

toate laturile sunt egale => ABCD romb sau patrat

latura =4√2 (u. l)

AC=√[(1-1)²+(-2-6)²)]= √64=8

BD=√[(5+3)²+(2-2)²)]= √64=8

Diagonalele sunt egale => ABCD e patrat

Aria ABCD=latura²=(4√2) ²=32 (u.a)