Question

Find the area of a rhombus if its vertices are A(3, 0), B(4, 5), C(−1, 4) and D(−2, −1). Also find the distance between its sides AB and CD.

Answer 1

Answer:

Area = 6 units² and the distance is 2.35 units.

Step-by-step explanation:

Find the length of diagonal 1 :

$\text {Length = }\sqrt{(Y_1 - Y_2)^2 + (X_1-X_2)^2}$

$\text {AC = }\sqrt{(4-3)^2 + (-1-0)^2}$

$\text {AC = }\sqrt{2}$

Find the length of diagonal 2 :

$\text {Length = }\sqrt{(Y_1 - Y_2)^2 + (X_1-X_2)^2}$

$\text {BD = }\sqrt{(-1-5)^2 + (-2-4)^2}$

$\text {AC = }\sqrt{72}$

Find the area:

Area = 1/2 (diagonal 1 x diagonal 2)

Area = 1/2 ( √2 x √72) = 6 units²

Find the length AB:

$\text {Length = }\sqrt{(Y_1 - Y_2)^2 + (X_1-X_2)^2}$

$\text {AB = }\sqrt{(5-0)^2 + (4-3)^2}$

$\text {AB = }\sqrt{26}$

Find the distance between AB and CD:

Let the distance be x

Area = 1/2 (base) (height)

6 = 1/2 (√26) (x)

x = 2.35 units

Answer: Area = 6 units² and the distance is 2.35 units.