Question

How do you find the area of the rectangle with vertices A(-5,1), B(-3,-1), C(3,5), D(1,7)?

Answer 1

consider rectangle ABCD as

A|----------|B

D|----------|C

it is very important to mark points in an order of clockwise or anticlockwise

(i have marked in clockwise direction)

so use distance formula

s=√(x2-x1)^2+(y2-y1)^2

area of rectangle=l*b

so l=AB;b=BC

so for AB

s1=√(-3+5)^2+(-1-1)^2

s1=√4+4

s1=2√2

similarly for BC

s2=√(3+3)^2+(5+1)^2

s2=√36+36

s2=√72

so area = l*b=s1*s2=(2√2)*√72

=2*√144

=2*12

=24 square units

hope this helps and u understand well :)