Question

Find the area of the figure below. Work should include explanations in words detailing how you simplify each specific radical. Include units in final answer. please

Answer 1

`A=70-510ft^(2)`

1) Note that this is a rectangle, so we can use the formula for the Area of a rectangle. So let's write it out and then plug into that the given measures:

`\begin{gathered} A=(-5√(2)+5√(5))(3√(2)+4√(5)) \\ A=(-5√(2)\cdot\:3√(2)-5√(2)\cdot\:4√(5)+5√(5)\cdot\:3√(2)+5√(5)\cdot\:4√(5)) \\ A=-15√(2^2)-20√(2)√(5)+15√(5)√(2)+100 \\ A=-30-20√(10)+15√(10)+100 \\ A=70-5√(10) \end{gathered}`

We can simplify those square roots and combine the terms with the same radical. So we can tell the area is:

`A=70-510ft^2`