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Lesson 1: Areas of parallelograms

# 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.
• I still don't really get it.
• To find the area of a parallelogram, you need the length of a base and the length of the height.

Area = base * height
• 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. :)
• i don't understand is a parallelogram many shapes or just one ?
• its one shape
• but how do you calculate the base and or height using this?
• If you know the area of the parallelogram and only `1` of either base or height, you can find the other by dividing area by that.

Examples:
Area `32` and height `8` => base `32/8 = 4`
Area `27` and base `3` => height `27/3 = 9`

It's basically working backwards from the Area formula.
Hope this helped!
• i do not get it :(. help me please
• Hey if you give me something a bit more specific I can walk you through it :)