Question

What is the area of rhombus ABCD ? Enter your answer in the box. Do not round at any steps. units² Rhombus A B C D on a coordinate plane with vertex A at 1 comma 0, vertex B at 7 comma negative 2, vertex C at 1 comma negative 4, and vertex D at negative 5 comma negative 2. Point P is at negative 3.8 comma 1.6. Dashed segments join point P to point D and point P to point A, forming right angle D P A.

Answer 1

Answer: 24 Units squared

Explanation:

Answer 2

We know, that when d₁ and d₂ are diagonals, then area of rhombus is:


`A = (1)/(2)\cdot d_1\cdot d_2`

In this case we have:


`d_1 = |7-(-5)|=|7+5|=|12|=\boxed{12}\\\\d_2 = |0-(-4)|=|0+4|=|4|=\boxed{4}`

so the area:


`A=(1)/(2)\cdot d_1\cdot d_2=(1)/(2)\cdot 12\cdot 4=6\cdot4=\boxed{24\,\,\text{units}^2}`