Question

The coordinates of rhombus abcd are a(-4,-2) b(-2,6) c(6,8) d(4,0). What is the area of the rhombus

Answer 1

First, graph the rhombus:

Area of a rhombus = Product of diagonals / 2

Find the length of the diagonals:

Distance between points:

`\sqrt[\placeholder{⬚}]{(x2-x1)^2+(y2-y1)2^}`

Diagonal AC

`AC=\sqrt[\placeholder{⬚}]{(6-(-4))^2+(8-(-2))^2}`

AC= 10√2

Diagonal BD

`BD=\sqrt[\placeholder{⬚}]{(4-(-2))^2+(0-6)^(^2)}`

BD=6√2

Area= AC x BD / 2

Area = [(10√2) x (6√2)]/2

Area = 60