The area of a rectangle is easy, remember? Length x width in square units, which is the same as base x height (b x h) in square units. Move that cut off triangle over to the right side and the parallelogram is suddenly a rectangle.
That means, no matter the angles we push and pull the parallelogram into, the four sides enclose the same area.Īnother way to think of it is to consider cutting off a triangle from, say, the left side of the parallelogram to leave a nice, perpendicular corner. At some point, we can make every interior angle a right angle and get a rectangle. That calculation seems too simple and does not seem to take into account the angled sides, does it?īut consider, we can move the parallelogram and change its angles.
Picture of parallelogram how to#
If you know the length of base b, and you know the height or width h, you can now multiply those two numbers to get area using this formula:Ī r e a = 162 i n 2 area=162i a re a = 162 i n 2 How to calculate the area of a parallelogram We need to find the width (or height) h of the parallelogram that is, the distance of a perpendicular line drawn from base CD to AB. The width (or height) of the crate – the distance straight across from the base to the other side – could vary depending on the inside angles of vertices A, B, C and D. The two short sides, at 12 inches, are BC and DA. Side CD forms the base ( b) of our parallelogram. The two long sides, at 18 inches, are AB and CD. The four vertices (corners) are A, B, C and D. We can name the various parts of our orange-crate parallelogram. Think of our wobbly orange crate we could nearly collapse it flat, but its two short sides would always be 12 inches. This is where things get tricky, because the distance along either short side is not necessarily its width. The length of any linear geometric shape is the longer of its two measurements the longer side is its base.įor any parallelogram, we need to know the length of a longer side (base), and its width. Finding the area of a rectangle, for example, is easy: length x width, or base x height. If you noticed the three special parallelograms in the list above, you already have a sense of how to find area. Its sides never change their length, but the crate's height (or width) changes. If you push or pull the crate so it leans more or less, every shape it takes is a parallelogram. If you turn the crate so one of its 18-inch sides is flat on a table, the crate naturally leans (because it had no bottom to hold the four sides rigid). Two of the crate's sides are 12 inches and the other two are 18 inches. Suppose you built a crate to hold, say, oranges, but you forget to put a bottom on it. Therefore, it can be said that every rhombus is a parallelogram, but the reverse is not possible.Three quadrilaterals, a rhombus, a square, and a rectangle are specific types of parallelograms. A rhombus itself is a special kind of parallelogram. On the contrary, the perimeter of the parallelogram can be calculated by – adding base and height, and multiplying the sum by 2.īoth parallelogram and rhombus are quadrilateral, whose facing sides are parallel, opposite angles are equal, the sum of the interior angles is 360 degree. The perimeter of rhombus can be calculated with the help of the following formula – 4 a, where a = side of the rhombus.Conversely, the area of the parallelogram can be calculated by multiplying base and height. The mathematical formula for the area of the rhombus is (pq)/2, where p and q are the diagonals.As opposed to a parallelogram whose diagonals bisect each other forming two congruent triangles. The diagonals of a rhombus bisect each other at right angles forming two scalene triangles.All the sides of the rhombus are equal in length whereas only the opposite sides of a parallelogram are equal.A parallelogram is a four-sided flat-shaped figure, whose opposite sides are parallel to each other. We define rhombus as a flat shaped, four-sided quadrilateral whose length of all sides congruent.The difference between rhombus and parallelogram can be drawn clearly on the following grounds: Key Differences Between Rhombus and Parallelogram
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