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How to Find The Area of Figures
Here are the area formulas that you'll need to know for the ACT
test. Every other area formula is usually given on the test.
Rectangle
To find the area of a rectangle, simply
multiply the base of the rectangle by its
height.
h
A = bh
b
Square
s
A = s2
To find the area of a square, multiply the
base of the square by its height (just like a
rectangle). In the case of a square,
however, since base and the height are the
same, all you need is the length of one of
the sides. To get the area, multiply the
length of the side by itself (or square it).
s
Paralleogram
To find the area of a parallelogram, multiply
the base times the height (just like a
rectangle).
h
A = bh
b
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Trapezoid
a
A=
h
a+b
2 h
To find the area of a trapezoid, add the
length of the two bases (the two parallel
sides), divide by 2 (which finds an average)
and then multiply by the distance between
the two parallel sides, or h.
b
Triangle
To find the area of any triangle, multiply 1/2
by the base of the triangle by the height.
Note that this works for any triangle and that
the height is not necessarily the length of a
side. It is the distance between the base
and the high point of the triangle (see
below).
A = 12 bh
h
b
A = 12 bh
h
b
Circle
r
A = πr2
To find the area of a circle, take the radius,
square it, and multiply that by pi. If you
have the diameter, instead of the radius,
divide it by half to get the radius, then
square and multiply by pi.
1
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Sometimes, you'll need to combine figures. For
example, in the figure on the left, you are asked to
find the area of the entire figure, which consists of a
square on the bottom, with a side of length 3, with a
triangle on the top with a height of length 2.
2
In order to solve, you would find would find the area
of the square (3 x 3 or 9 square units) and add it to
the area of the triange (1/2 x 3 x 2 or 3 square units)
for a total of 12 square units.
3
1
A = 32 + (3)(2)
2
or
1
A = 9 + (6)
2
On these types of problems, it's best to try and break
it down into a combination of the figures that you
have the formulas for and see if you can determine
the missing pieces of information (such as the length
of the base of the triangle in the problem above. You
know its base, even though not explicitly given,
because it is one of the sides of a square and you
have the length of one of the sides
or
A=9+3
or
A = 12
You'll also need to subtract figures sometimes. A
common problem is the following:
You have a circle that is circumscribed in a square.
Find the total area in the square that is not part of the
circle (the shaded portion).
4
2
4
A=4 −π
2
To do this types of problem, all you need to do is
calculate the area of the square, the area of the circle,
and subtract the circle's area from the square's area.
You'll be left with the area of the shaded portion.
2
or
A = 16 − π 22
1
or
A = 16 − 4π
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