Question

Find the area of the trapezoid. points are (-5,-3)(4,-3)(6,-7)(-7,-7)​

Answer 1

44 square units

Explanation:

The area of a trapezoid with bases b₁ and b₂ and height h is given by the formula

`A=\left((b_1+b_2)/(2)\right)h`

If you're wondering how we get this formula, check the attached illustration (remember the area of a parallelogram is its base multiplied by its height)! Moving on to our trapezoid, the pairs of points (-5,-3)(4,-3) and (6,-7)(-7,-7) form two horizontal segments, which form b₁ and b₂, and our height is the distance between the y-coordinates -3 and -7, which is 4. We can find b₁ and b₂ by finding the distance between the x coordinates in their pairs of points:

`b_1=|-5-4|=|-9|=9\\b_2=|6-(-7)|=|6+7|=13`

Putting it altogether:

`A=\left((9+13)/(2)\right)(4)=\left((22)/(2)\right)(4)=(11)(4)=44`

So the area of our trapezoid is 44.