Question

The coordinates of rhombus ABCD are A(–4, –2), B(–2, 6), C(6, 8), and D(4, 0). What is the area of the rhombus? Round to the nearest whole number, if necessary.

Answer 1

Answer:

The rhombus ABCD has an area of 22 square units.

Step-by-step explanation:

The coordinates of rhombus ABCD are shown in the image attached below. The area of the rhombus can be found in terms of their diagonals, which are now calculated by Pythagorean Theorem:

$AC = \sqrt{[6-(-4)]^{2}+[8-(-4)]^{2}}$

$AC = 15.620$

$BD = \sqrt{(4-6)^{2}+[0-(-2)]^{2}}$

$BD \approx 2.828$

The area of the rhombus is: ($AC = 15.620$ and $BD \approx 2.828$)

$A = \frac{AC\cdot BD}{2}$

$A = \frac{(15.620)\cdot (2.828)}{2}$

$A = 22.087$

The rhombus ABCD has an area of 22 square units.