If the area of a square is 144, what is the perimeter of the square? If a square and a circle have the same perimeter, which of them will have a greater area?
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In the parallelogram above, we drew a perpendicular line from one vertex to the opposite side, then cut that piece off of the parallelogram, and added it to the other side of the parallelogram to create a rectangle. Can the pieces of a parallelogram always be combined like this to create a rectangle?

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A parallelogram is converted to a rectangle by cutting and rearranging pieces of the shape, as shown above. Given that the area of a rectangle is \(\text{(base)}\times\text{(height)},\) is the area of a parallelogram also \(\text{(base)}\times\text{(height)}?\)

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Two identical trapezoids combined to form the parallelogram, so the area of the trapezoid is half of the area of the parallelogram. Given the base lengths of Base 1 and Base 2, what is the area of the trapezoid?

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A trapezoid can be cut into two pieces and arranged into a parallelogram as shown. The two figures have the same area. Does this expression represent the area? \[\frac{1}{2}(h)(x + y)\]

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