Question

What is the area of rhombus ABCD ?

Enter your answer in the box. Do not round at any steps.

Answer 1

it would be 4 times 4 which equals 16

Answer 2

we know that

To find the area of a rhombus, multiply the lengths of the two diagonals and divide by two

so

`A=(1)/(2)(d1*d2)`

where

d1 and d2---------> are the lengths of the two diagonals

In this problem the diagonals are

AC and DB

The formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Step 1

Find the distance AC

`A(-1,4)\ C(-1,0)`

substitute in the formula

`d=\sqrt{(0-4)^(2)+(-1+1)^(2)}`

`d=\sqrt{(-4)^(2)+(0)^(2)}`

`dAC=4\ units`

Step 2

Find the distance DB

`D(-5,2)\ B(3,2)`

substitute in the formula

`d=\sqrt{(2-2)^(2)+(3+5)^(2)}`

`d=\sqrt{(0)^(2)+(8)^(2)}`

`dDB=8\ units`

Step 3

Find the area of the rhombus

`A=(1)/(2)(d1*d2)`

we have

`d1=dAC=4\ units`

`d2=dDB=8\ units`

substitute the values

`A=(1)/(2)(4*8)=16\ units^(2)`

therefore

the answer is

`16\ units^(2)`