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Lesson 2: Area of parallelograms and triangles

# Area of a parallelogram

Discover the magic of geometry! The area of a rectangle and a parallelogram can be calculated in the same way. Just multiply the base by the height! This simple trick works because a parallelogram can be rearranged into a rectangle. Geometry is full of surprises!

## Want to join the conversation?

• I have two questions:
1. Does this work for all quadrilaterals?
2. Why is there a 90 degree in the parallelogram?
• 1. No, this only works for parallelograms
2. A parallelogram is defined as a shape with 2 sets of parallel sides, so this means that rectangles are parallelograms. By definition rectangles have 90 degree angles, but if you're talking about a non-rectangular parallelogram having a 90 degree angle inside the shape, that is so we know the height from the bottom to the top. It has to be 90 degrees because it is the shortest length possible between two parallel lines, so if it wasn't 90 degrees it wouldn't be an accurate height.
• I have 3 questions:

1. Dose it mater if u put it like this: A= b x h or do you switch it around?

2. Will it work for circles?

3. How many different kinds of parallelograms does it work for?

And may I have a upvote because I have not been getting any.
• It doesn't matter if u switch bxh around, because its just multiplying. When you multiply 5x7 you get 35. If you multiply 7x5 what do you get? You get the same answer, 35.

2.There is a diffrent formula for a circle, triangle, cimi circle, it goes on and on. The formula for circle is:
A= Pi x R squared.
• What is the formula for a solid shape like cubes and pyramids?
• Nice question!

For 3-D solids, the amount of space inside is called the volume. Volume in 3-D is therefore analogous to area in 2-D.

The volume of a cube is the edge length, taken to the third power. The volume of a rectangular solid (box) is length times width times height. Note that these are natural extensions of the square and rectangle area formulas, but with three numbers, instead of two numbers, multiplied together.

The volume of a pyramid is one-third times the area of the base times the height. Note that this is similar to the area of a triangle, except that 1/2 is replaced by 1/3, and the length of the base is replaced by the area of the base.
• 1. Does it work on a quadrilaterals?
2. Can this also be used for a circle?
Sorry for so my useless questions :(
• The formula for quadrilaterals like rectangles
and parallelograms is always base times height.
The formula for a circle is pi to the radius squared.
Also these questions are not useless. :)
• whats the point of this stuff? its not like were gonna use in in life and why does we always say "WhEn I Do ThIs YoUr GoNnA sEe SoMeThInG AmAzInG" like broits so annoying
• unless u want to be homeless u have to take the SAT which contains these stuff
• i don't understand is a parallelogram many shapes or just one ?
• its one shape
• I thought to find area you use length x width to figure it out.
• Sal put base instead of width probably to make people understand more easly about Parallelogram (I have a hard time saying width)
• Great but doesn't answer my question. What are the properties of parallelogram?
• A parallelogram is defined as a quadrilateral with two pairs of parallel sides. This implies the following properties:

1. Pairs of opposite (parallel) sides are equal.
2. Pairs of opposite angles are equal.
3. Any two consecutive angles sharing a common side are supplementary (that is, they add to 180 degrees).
4. The two diagonals intersect at their common midpoint.
5. Each diagonal alone divides the parallelogram into two congruent triangles.
6. The two diagonals together divide the parallelogram into two pairs of congruent triangles.

Have a blessed, wonderful day!