Please help! How do you find the surface area of a flat shape? >~<

1 Answer
CountryGirl
May 2, 2018

Please see below:

Explanation:

There are many different formulas to find the areas of different shapes. Here are a couple shapes and examples:

#" " " " " " " " " " " " " "# RECTANGLES:
enter image source here

Rectangle area is ALWAYS: #color(red)"width"# #xx# #color(red)"height"#

Say you have a rectangle with a width of #4# and a height of #8# what is the area?

#"width"# #xx# #"height"#

#4 xx 8#

#32#

The area is #32# #"un"^2#.

#" " " " " " " " " " " " " "# TRIANGLES

enter image source here

Triangle area is ALWAYS: #color(red)(1/2)# #color(red)"base"# #xx# #color(red)"altitude"#

Say you have a triangle with a base of #5# and an altitude of #9#. What is it's area?
#1/2# #"base"# #xx# #"altitude"#

#1/2(5)(9)#

#1/2(45)#

#22.5#

The area of the triangle #22.5# #"un"^2#.

enter image source here

What about a triangle that is a little weirder? Well, no matter the shape of the triangle, the area is ALWAYS half the altitude times the base.

#1/2# #"base"# #xx# #"altitude"#

#1/2 (14)(8)#

#1/2(112)

#56#

The area of this triangle is #56# #"un"^2#

#" " " " " " " " " " " " " " " " " " # SQUARES

Squares are types of rectangles, so you can get their area by using the formula:

#"width"# #xx# #"height"#

But squares are special because their width and height are always the same, so the special formula for squares is:

#color(red)"side"^color(red)2# (this means #"side"# #xx# #"side"#)

enter image source here

What is the area of a square with a side of #6#?

#"side"^2#

#6^2# (#6 xx 6#)

#36#

The area of this square is #36# #"un"^2#.

I hope this has helped you with a couple basic shapes. If you want another type of shape, feel free to leave it down in the comments and I can update the answer :)

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