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Area is the quantity that expresses the amount of surface a two-dimensional shape covers in square units.

Area is the measure of the surface of a two-dimensional figure.

The area of a shape can be measured by comparing
the shape to squares of a fixed size, called unit squares.
The unit square can represent different units of measure.
It could be 1 foot by 1 foot.
1 centimeter by 1 centimeter
1 inch by 1 inch, and so on.
unitsquare
unitinch

The example at the left shows a rectangle divided into 8 unit squares where each unit square represents 1 square inch.

The area of the rectangle is 8 square inches.

Not all figures can be divided into an exact number of unit squares. Consider the diagram at the right.

A grid, with each square on the grid representing 1 sq. cm., is laid out to show the location of the unit squares.

Six of the unit squares have been cut diagonally, which means cut in half regarding area.

The area of the figures is 9 full unit squares plus 6 half unit squares = 12 square cm.

unitslant

unittri

In the diagram at the left, we see 6 full unit squares inside the triangle.

But, we do not know how the other unit squares have been divided. They are not cut along their diagonals which would cut them in half.

Since this is a right triangle, we can create a rectangle around the triangle such that our triangle is half of the rectangle in area.

Area of rectangle = 18 square inches.
Area of triangle = 9 square inches.

Not all diagrams can be easily solved by examining the number of unit squares that can be drawn inside the figure.

The triangle in the diagram at the right is not a right triangle. We cannot draw a rectangle around this triangle such that the area of the triangle will be half of the area of the rectangle.

Yes, we could draw a rectangle, and then draw two more rectangles around the "outer" triangles, but things are now getting messy to visualize.

A formula is a better solution.     A = ½bh
Area of triangle = ½ • 6 • 4 = 12 square meters.

unittri2

When working with area, you need to know the area formulas
of some basic geometric shapes. You can then use these formulas,
alone or in conjunction with other formulas, to find the area of a figure.

The colored (or painted) surface of the figure represents the area.
Remember to label areas with "square units".

areatri
Area (all triangles)
areatri
areaequitri
Area (equilateral triangle)
areaeqitri
arearect
l = length and w = width may also be used
Area (rectangle)
areabh
arealw
areasq
Area (square)
areasq
areapar
Area (parallelogram)
areapara
areatrap
Area (trapezoid)

areatr
arearh
d1 = diagonal 1; d2 = diagonal 2
Area (rhombus)
arearho
Area can also be calculated with A = bh.

 

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