Parallelograms are quadrilaterals with opposite sides that are parallel to each other. The area of a parallelogram is the width times the length.
Parallelograms can be modified into different shapes, and all have their own formulas for area. For example, a rhombus has an A = lw formula, where l is the length and w is the width.
Knowing how to find the area of a parallelogram can be very useful in calculating the area of shapes that are close to being parallelograms. How? Well, you will have to find the average of the dimensions and then calculate using that average as one of the dimensions!
This article will go more in depth on how to find the area of a parallelogram with specific examples.
Calculate the angles in the corners
The first step in finding the area of a parallelogram is to calculate the angles in each corner. You can do this by using the angle formula for triangles:
180° – Ax = Angle A
180° – Bx = Angle B
180° – Cx = Angle C
where x is the length of one side of the triangle. To make things easier, you can divide all sides by two, so that x equals one. This way, you only have to calculate half of the angles, which are A and B.
So far we have: A=90−Ax and B=90−Bx. Now we can add these together to get the total angle in each corner: A+B=180.
Find the area using the formula
The final step in this problem is to find the area of the parallelogram. The area of a parallelogram is found by multiplying the height by the base.
In this problem, the height is found by dividing the difference between the greatest and least heights by 2. This gives you a height of 3.
The base is found by adding up all of the bases and dividing by 2. The bases add up to 20, so your final answer is .
You did it! You found the area of a rhombus with vertices A(−3, 0), B(−1, 5), C(7, 4), and D(5, −1). You can also use this method for any other type of quadrilateral.
Re-draw the parallelogram with a ruler and pencil
Next, re-draw the parallelogram using a pencil and ruler. You can use any type of pencil, but a sharpened no. 2 is recommended.
A no. 2 pencil has a thick enough lead that it can easily draw the lines of the parallelogram and cover the entire figure. A no. 1 pencil would be too thin and might break when drawing the lines, and a no. 3 pencil would be too thick, making it difficult to draw the lines properly.
The ruler must be a standard ruler with sides of equal length. A square or rounded-edge ruler will not work for this part of the problem! You will have to use a straight edge to draw the lines of the new parallelogram.
Measure the area using a calculator
You can also use a calculator to find the area of a parallelogram. First, enter the numbers into the calculator as pairs of numbers that make up the sides of the parallelogram.
Then, press one of the buttons that says “area” or “perimeter” and let the calculator figure it out. Most calculators require you to set up at least two of the sides as opposite pairs, which is why we included those in this problem.
The area of a parallelogram is always equal to half of its perimeter multiplied by its height. This is an easy way to figure out the area using the perimeter and one side of the shape.
Confirm your results by recalculating them
Once you have calculated the area of a parallelogram, you should confirm your results by recalculating them. You can do this by calculating the area of a rectangle with the same length sides as the parallelogram.
If the width of the rectangle is equal to one of the parallelogram’s sides, then you can use the formula for the area of a rectangle to calculate this second area.
You can also do this by calculating the area of a triangle formed by two adjacent edges of the parallelogram and a common vertex. Then, calculate the area of a square with one side equal to one side of the parallelogram. Add these areas together to get the total area.
Compare these areas to that of the parallelogram to confirm your answer.
Share your final answer with others
Once you have an answer, make it a point to share it with others. You can do this in many ways. You can talk about it in person or on a podcast, you can write an article about it, or you can create a blog post where you explain your answer.
It is important to share your answer because then other people can learn from what you learned. You may have even learned something new while researching your answer!
As mentioned earlier, the area of a parallelogram is dependent on the lengths of its sides and not its orientation. This makes it easy to identify the area of a parallelogram if given the right information.
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