Question

Use the distance formula to find the area of the rectangle

Answer 1

Answer:

Therefore Area of Rectangle is 50 unit².

Step-by-step explanation:

Given:

Let the vertices of a Rectangle be

A ( -1 , 7)

B ( 4 , -3)

C ( 0 , -5)

D ( -5 ,5)

To Find:

Area of Rectangle ABCD = ?

Solution:

First we will find the Length and Width of Rectangle by Distance Formula ,

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

Substituting the values we get

$l(AB) = \sqrt{((4-(-1))^{2}+(-3-7)^{2} )}$

$l(AB) = \sqrt{((5)^{2}+(-10)^{2} )}\\l(AB)=\sqrt{125}=5\sqrt{5}\ unit$

Similarly for BC we will have,

$l(BC) = \sqrt{((0-4)^{2}+(-5-(-3))^{2} )}\\l(BC)=\sqrt{20}=2\sqrt{5}\ unit$

Now

$Length=AB =5\sqrt{5}\ unit\\Width=BC=2\sqrt{5}\ unit$

Now Area of Rectangle is given by

$\textrm{Area of Rectangle}=Length\times Width$

Substituting the values we get

$\textrm{Area of Rectangle ABCD}=5\sqrt{5}\times 2\sqrt{5}=10\times 5=50\ unit^{2}$

Therefore Area of Rectangle is 50 unit².