Question

10. rhombus abcd has vertices at a(-2, 7), b(8, 7), c(2, -1), and d (-8, -1).

determine the area of abcd.

Answer 1

Answer: 80

Explanation:

We can use the formula
`A=(d_(1)d_(2))/(2)`, where
`d_(1), d_(2)` are the lengths of the diagonals.

By the distance formula,

`AC=\sqrt{(-2-2)^(2)+(-1-7)^(2)}=√(16+64)=4√(5)\\BD=\sqrt{(-8-8)^(2)+(-1-7)^(2)}=√(256+64)=8√(5)`

So, the area is
`((4√(5))(8√(5)))/(2)=\boxed{80}`