Calculating Area Measuring the surface in squares
AREA is a measure of a surface using squares. The size of the square is determined by the linear units used to measure the length of the sides of the object. As an example, if the sides of a square object measure 1 foot long each, then the surface area is side x side or 1 square foot. The same object measured in inches is 12 inches by 12 inches which equals 144 square inches.
Notice that the length of the sides (measured in linear units) is a measure of how long the line is. Also notice that the two sides meet at a right angle (90°)
Areasquare = side x side -or- A = s x s -or- A = s²
These two pieces of information are needed for all calculations of area: a) two linear dimensions which b) meet at a 90° angle.
Let's consider some other shapes:
The rectangle is easy - it has two dimensions at 90° angles. The sides are 7 units high by 17 units wide (We use the term 'units' when we do not know what units are being used). Notice that these measures tell us how long each side is. We can now either count how many square units there are, or we can calculate it by multiplying 7 x 17 which gives us 114 squares or square units or units² (abbreviated un²).
Arearectangle= length x width -or- A = lw
The parallelogram is next. While the sides do not meet at 90° angles, when we look at the picture, we can see that how high the parallelogram is can be found by counting straight up from the bottom or base.
Areaparallelogram=base x height -or- A = bh
We can see how this works by cutting one side of the parallelogram off along a line that goes from the top to the bottom (base) and mets at a 90° angle. This piece can be attached to the other end and creates a rectangle (or maybe a square, depending on the shape). For parallelograms we call the height height and the bottom side we call the base. We can now count the number of squares (square units) or once again, multiply the base x the height (7 x 14) and get the area of 98 square units or 98 un².
Areatriangle=(base x height) ÷ 2 -or- A = (bh) ÷ 2
That leaves us with 2 shapes to consider: the trapezoid and the circle. We will do the trapezoid here and the circle on a separate page.
- Cut the trapexoid in half the long way
- Separate the top half
- Turn the top half over and
- Attach to the end aof the bottom half
- mark the height and separate the end
- Move to the other end and attach, forming a rectangle
We can now count the number of squares (square units) or once again, multiply the base x the height to find the area.
Method #2:
This method is like the triangle method - but remember - you have to divide by 2 to get the area of ½ the figure!
Here are all of the formulas for these figures:
