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Geometry – Area Problems

Every ACT test that I have seen include several problems that require you to calculate the area of a figure, usually rectangles, squares, parallelograms, triangles, trapezoids, and circles.  Area problems that require multiple calculations of area that are either combined or subtracted are also common. Because area problems are so common, let’s review the area formulas.

Area of Rectangles

The area of a rectangle is calculated by multiplying the base of the figure and its height or Area = base x height.

Area of Squares

The square is a unique four-sided figure, since all sides have the same length and so the area of a square is equal to the length of a side, squared or Area = side x side = side^2;

Area of Parallelograms

The area of a parallelogram is calculated the same as the area for a rectangle in that it is found by multiplying the base times the height or Area = base x height.  Note that the height is not the length of the one of the non-parallel sides, but the height of the parallelogram.  Think of it as the distance between the top side and the bottom side.

Area of Triangles

The area of a triangle is found by multiplying base of the triangle by the height and then dividing by two or Area = 1/2 x base x height.  Like the parallelogram, don’t assume that the length of one of the sides is necessarily the height.  It may be, if it is a right triangle.  The height is the distance between the base and the top point of the triangle.

Area of Trapezoids

The area of a trapezoid is calculated by adding the length of the two parallel lines together, dividing by two, and then multiplying by the height or A = (b1+b2)/2 x h.

Area of Circles

The area of a circle is found by squaring the length of the radius and then multiplying by π or A = π r^2.

Area of other Figures

In the analysis that I’ve done, if there are other figures on the ACT test where you need to calculate the area of the figure, you are given the formula in the test.  So don’t stress about that too much.

Note that you are also frequently required to find areas in a problem by adding or subtracting the areas of one or more figures.  In those cases, calculate the area of each individual figure and then calculate the requested area.

To help you out, I’ve prepared a free report, Area of Plane Figures, with more detailed information and examples on calculating the area of plane figures.  Let me know if this helps you, or if  you have more questions.

Scott

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