Question

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

Answer 1

Answer: 80

Step-by-step explanation:

We can use the formula $A=\frac{d_{1}d_{2}}{2}$, where $d_{1}, d_{2}$ are the lengths of the diagonals.

By the distance formula,

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

So, the area is $\frac{(4\sqrt{5})(8\sqrt{5})}{2}=\boxed{80}$