Making Algebra easier for you!

Area is the number of square units **inside** of a
shape. We typically find the area of a shape that is two dimensional
(like a floor, or a piece of carpet, or a piece of land).

Since the area is measuring the number of square units inside of the shape, the units must be written as squared units (ex: cm^{2}).

Many of the area formulas require you to know the **height** of the shape.

The height of the shape is always the **distance from the top of the shape to the bottom.** The height must be a **straight**, vertical line.

Keep this page handy as you study formulas and solve real world problems throughout your algebra studies!

A square has 4 sides that are all exactly the same size. Therefore, finding the area is pretty easy! Since the area of a square or rectangle is length x width, we can just square the length of the side! Take a look!

Area of a Rectangle

A rectangle is a 4 sided figure with two pairs of parallel lines. Each set of parallel lines has the same length. To find the area of a rectangle we are going to multiply the length x the width.

Area of a Parallelogram

A parallelogram is another 4 sided figure with two pairs of parallel lines. To find the area of a parallelogram, we will multiply the base x the height. Let's look at the formula and example.

**Notice that we did not use the measurement of 4m. 4m did not
represent the base or the height, therefore, it was not needed in our
calculation.**

Area of a Trapezoid

A trapezoid is a 4 sided figure formed by one pair of parallel sides. This area formula is a little more complicated. Study the example carefully!

**Take note that the bases of a trapezoid are always the parallel lines.**

Area of a Triangle

A triangle is a 3 sided figure. There are several different types of
triangles. You must be careful when trying to locate the height of the
triangle. ** Remember the height of the shape must be a straight, vertical line.**

**Again, notice that we did not need to use the measurement of
11cm. 11cm did not represent the base of the triangle, nor did it
represent the height.**

** You will not always need to use every measurement that is given in the problem.

A circle, of course, has no straight lines. We use pi (3.14) when we calculate the area of a circle.

What Would Happen if We Were Given the Diameter of the Circle and Asked to Find the Area?

f you are given the diameter of a circle (which is the distance
across the circle - through the center), then you would divide the
diameter in half. One-half of the diameter = the radius.

Don't forget that the area is a measurement of the inside space of a two dimensional figure. We are measuring how many "square units" fit on the inside.

I hope that these formulas have helped you to solve your algebra problems. Good luck!

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