Question

Find the area of the trapezoid. If the answer is not an​ integer, leave it in simplest radical form. The figure is not to scale.

Answer 1

We have been given an image of a trapezoid. We are asked to find the area of the given trapezoid.

We will use area of trapezoid formula to solve our given problem.

`A=(1)/(2)(a+b)* h`, where,

A = Area of trapezoid,

a and b = Parallel sides or bases of trapezoid.

h = Height of trapezoid.

We can see that one base is 45 feet. The other base would be 45 plus 15 feet that is
`45+15=60`.

Now we will use Pythagoras theorem to find the height of the trapezoid as:

`h^2=17^2-15^2`

`h^2=289-225`

`h^2=64`

`√(h^2)=√(64)`

`h=8`

`A=(1)/(2)(45+60)* 8`

`A=(105)* 4`

`A=420`

Therefore, the area of the given trapezoid is 420 square feet.