Question

What is the area of rhombus ABCD?

Enter your answer in the box. Do not round at any steps.
units²
-5
D(5,-2)
4
-2
1
M
-2
4
-5
A(1,0)
C (1.-4)
3
4
5
6
7
8
B(7,-2)
9

Answer 1

The area of rhombus ABCD is 4 units²

Explanation:

To find the area of a rhombus, we can use the formula:

Area = (diagonal 1 * diagonal 2) / 2

Given the coordinates of the vertices A(1, 0), B(7, -2), C(1, -4), and D(5, -2), we can calculate the diagonals using the distance formula:

Diagonal 1 = distance between points A and C Diagonal 2 = distance between points B and D

Using the distance formula, the calculations are as follows:

Diagonal 1: √[(x2 - x1)² + (y2 - y1)²] √[(1 - 1)² + (-4 - 0)²] √[0 + 16] √16 = 4

Diagonal 2: √[(x2 - x1)² + (y2 - y1)²] √[(5 - 7)² + (-2 - (-2))²] √[(-2)² + 0²] √[4 + 0] √4 = 2

Now, we can substitute the values of the diagonals into the area formula:

Area = (diagonal 1 * diagonal 2) / 2 Area = (4 * 2) / 2 Area = 8 / 2 Area = 4