Question

Question #0a6f5

Answer 1

`\text{Area}=350\sqrt{2}`

`\text{Length of non-parallel side}=15`

Explanation:

Perimeter is defined as the sum of all the sides (boundaries) of a geometric figure.

Since a trapezoid has four sides and we are given with two of the sides, it is clear that the other two non-parallel sides are equal in measure.

Let's say `x` represents the length of each non-parallel side.

So, we have:

`\text{Perimeter}=2x+40+30`

`\text{100}=2x+40+30`

Solve for `x` to get:

`x=15`

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Now draw a right triangle to solve for the height. The dimensions of the triangle would be:

`\text{Hypotenuse=15}` `" "` `\text{Adjacent}={40-30}/2=5`

`\text{Height}=h=\sqrt{15^2-5^2}`

`h=10\sqrt{2}`

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Find the area of the trapezoid by applying the formula:

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`\text{Area} = \frac{40+30}{2}\cdot 10\sqrt{2}`

Simplify:

`=350\sqrt{2}`

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That's it!