One side of the trapezoid is 10 inches. the side parallel to this is twice as long as this side. the height is half as long as the given side length. find the area of the trapezoid

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/ ___ \  Let's imagine a trapezoid looks like this. The two parallel lines would be the top and the bottom lines.

The 10 in. side would be either the top or bottom line. The other parallel line is twice as long, meaning it's 2 times longer. So you multiply 10 in x 2 = 20 in.

The given side length = 10 inches.
Height = half as long, meaning it's half of 10 in. = 5 in.

Formula of a trapezoid =  x height
Where a and b are bases. The top and bottom of the trapezoid are bases.

Area trapezoid =  x 5 =  x 5 = 15 x 5 = 75 in²  <-- area means the unit is squared