Question

A rectangle has vertices at (-1,6), (-1,-2), (3,6), and (3,-2). Sara says the area of the rectangle is 16 square units and her

work is shown below
Steps
Step 1
Step 2
Step 3
Sara's Work
Base: 113-4
Height: 161+F2-4
Area: 4x4-16 square units
Where, if at all, did Sara first make a mistake in finding the area of the rectangle?
Step 1
Step 2
Step 3
no mistake

Answer 1

step 2

Explanation:

Answer 2

Step 2

Explanation:

Let

`A(-1,6), B(-1,-2), C(3,6), D(3,-2)`

Plot the vertices to better understand the problem

see the attached figure

The area of the rectangle is equal to

`A=bh`

we have

`b=BD\\ h=BA`

step 1

Find the base b (BD)

`B(-1,-2),D(3,-2)`

`b=\left|3\right|+\left|-1\right|=4\ units`

step 1 is correct

step 2

Find the height h (BA)

`B(-1,-2),A(-1,6)`

`h=\left|6\right|+\left|-2\right|=8\ units`

step 2 is not correct

step 3

Find the area

`A=(4)(8)=32\ units^(2)`

Therefore

Sara first make a mistake in finding the area of the rectangle in Step 2