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The area of a parallelogram is equal to base times height. You can find the maximum area of a parallelogram by multiplying the length of a short side by the length of a long side. (This would be the area if the parallelogram were a rectangle.)

You cannot know the area of a parallelogram if all you know is the length of the sides; you can only know the maximumpossible area. Imagine you slant the parallelogram a lot. The area will decrease, but the side lengths will stay the same.

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Q: How can you find the area of a parallelogram if you only know the side lengths?

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If you know its area then divide its height into the area which will give the length of the base of the parallelogram

You can if you know the lengths of the two pairs of sides. Thanks to the fact that sin(30) = 0.5, the height of the parallelogram is half the length of the sloping side.

You would need to know its side lengths and angles and then you can compute height

If and when two parallelograms are similar, you know that the ratio of two side lengths within one parallelogram will describe the relationship between the corresponding side lengths in a similar parallelogram. If and when two parallelograms are similar, you know that the ratio of corresponding side lengths in the other parallelogram will give you the scale factor that relates each side length in one parallelogram to the corresponding side length in a similar parallelogram.

It depends on what information you DO have.

That depends upon what you know about the parallelogram. If you know the area and base length, then: area of parallelogram = base X height height =area / base If you know the lengths of the two pairs of parallel sides and the angles, then trigonometry can be used. If the height is required between one pair of sides, then: height = other_side_length / sine(angle_between_sides)

Its length and its perpendicular height Area = length*height

You cannot. You need to know, or be able to calculate, its [perpendicular] height and information about the side lengths is not enough to determine that.A parallelogram can be flexed into a rectangle (when its area is maximised) to a long thin shape with area tending to zero.

Not exactly. If I know the side lengths, I can still find the perimeter

There is no exact formula to find the area of a parallelogram * * * * * It all depends on what information you do have. If you know the base length, B, and the vertical height, H, then the area is B*H square units. If you don't know H but know an angle then some trigonometry will enable you to find H.

For the perimeter, you just go round the shape, adding the lengths of each side as you go along. There may or may not be simple formulae of the area for a shape with unequal sides. If all you know is the [different] side lengths then only a triangle has a relatively simple formula for its area. If you also know that some of the sides are parallel, then you can find the area of a rectangle. Then, if you also know the perpendicular distance between the parallel sides, you can do a parallelogram. If, in addition you know which sides are parallel, a trapezium. And so on.

You can find the permeter if you know the length of the sides. You need to add the lengths of all the sides together.

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