Question

What is the area of the rectangle shown on the coordinate plane?

Answer 1

The area of the rectangle would be 21 units.

Answer 2

The area of rectangle is 42 square unit.

Explanation:

We are given a rectangle shown in diagram.

We need to find the area of rectangle.

`\text{Area of rectangle }=L* B`

First we have to find the L and B of the rectangle.

Using coordinate system find the coordinate of vertex of rectangle.

Using distance formula to find the distance of leg of rectangle.

A(2,-1) B(9,-8) C(12,-5)

Distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`L=AB=√((2-9)^2+(-1+8)^2)=7\sqrt2`

`B=BC=√((12-9)^2+(-5+8)^2)=3\sqrt2`

`\text{Area of rectangle }=7\sqrt2* 3\sqrt2 = 42\text{ Square Unit}`

Hence, The area of rectangle is 42 square unit.