Question

What is the area of rectangle ABCD in square units ?

Answer 1

Answer:

34 square units

Explanation:

In any rectangle, each two opposite sides are equal

This means that, in the given rectangle:

AB = CD and AD = BC

Area of the rectangle is the product of its dimensions (length and width)

This means that:

Area of ABCD = AB × BC

1- getting the side length:

To get the side length, we will use the distance formula:

$D = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

For AB, we have:

A = (-1,4) which means that x₁ = -1 and y₁ = 4

B = (3,3) which means that x₂ = 3 and y₂ = 3

Substitute in the equation:

$AB = \sqrt{(3-(-1))^2+(3-4)^2} = \sqrt{17}$ units

For BC, we have:

B = (3,3) which means that x₁ = 3 and y₁ = 3

C = (1,-5) which means that x₂ = 1 and y₂ = -5

Substitute in the equation:

$BC = \sqrt{(1-3)^2+(-5-3)^2} = 2\sqrt{17}$ units

2- getting the area:

Area of ABCD = AB × BC

Area of ABCD = $\sqrt{17} * 2\sqrt{17} = 34$ square units

Hope this helps :)

Answer 2

Answer:

Step-by-step explanation:

Square units = √( 4^2 + 1^2) * √( 8^2 + 2^2)

= √17 * √68

= √1156

= 34