Question

Use the distance formula to find the area of the rectangle

Show work to receive credit

Area=_______

Answer 1

Therefore Area of Rectangle is 50 unit².

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)=√(125)=5√(5)\ unit`

Similarly for BC we will have,

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

Now

`Length=AB =5√(5)\ unit\\Width=BC=2√(5)\ unit`

Now Area of Rectangle is given by

`\textrm{Area of Rectangle}=Length* Width`

Substituting the values we get

`\textrm{Area of Rectangle ABCD}=5√(5)* 2√(5)=10* 5=50\ unit^(2)`

Therefore Area of Rectangle is 50 unit².