Parallelograms are quadrilateral shapes with opposite sides that are parallel to each other. The area of a parallelogram is the size of the shape measured by the length of the bases and the width.
The width of a parallelogram is always considered to be 0, as the sides are parallel and therefore have no length. The length of the bases can be determined by any pair of points on the parallelogram.
Determine the area of a parallelogram by first identifying its vertices (endpoints) and then calculating the area of a rectangle based on the length of its bases and its height. Then, subtract the areas of the rectangles to find the area of the parallelogram.
This blog post will discuss how to find the area of a parallelogram with particular vertices.
Find the width of the parallelogram
The width of the parallelogram is the distance between point A and point D, or 3 units. The width of the parallelogram is also the distance between point B and point C, or 1 unit.
The total width of the parallelogram is therefore 4 units. We will call this value w.
Now that we have the value of w, we can find the area of the parallelogram. Area is defined as length × width, so we can write area = length × width.
We know the length of the parallelogram, which is represented by l, so we can write our equation as A = lw.
Calculate the height of the parallelogram
The next step in calculating the area of a parallelogram is to calculate the height of the parallelogram. The height of a parallelogram is the perpendicular distance from the bottom parallel line of the parallelogram to the opposite side.
To calculate the height of the parallelogram, you must first calculate the length of one of its sides and then subtract the length of the other side.
The length of one side is simply any one of the sides of the rectangle that makes up part of this shape. In this case, take the side with value 5 and make it your hypotenuse (the long side opposite the right angle).
Subtract 3 from 5 to get 2 as your hypotenuse. Multiply that by 2 to get 4 as your height.
Calculate the area of the parallelogram
The area of a parallelogram can be calculated with the following formula:
area of parallelogram = base × height
Where the base is the length of one side, and the height is the length of the opposite side.
In this problem, there are four bases and one height, so you need to decompose each component to find their respective bases and heights. Once you have those, combine them using the formula above.
The first component is one side of the parallelogram. The length of this side is three units. Because this side is a diagonal, its height is zero. Thus, we can decompose this component as follows: base × height = 0 × 0 = 0 .
The second component is another side of the parallelogram. The length of this side is five units. Because this side is a diagonal, its height is two units. Thus, we can decompose this component as follows: base × height = 5 × 2 = 10 .
The third component is another side of the parallelogram. The length of this side is one unit. Because this side is a diagonal, its height is zero units. Thus, we can decompose this component as follows: base × height = 1 × 0 = 0 .
Confirm your calculations
Once you have the area of your parallelogram, you can confirm your answer by calculating the area of the triangle and subtracting that from the total area.
The formula for the area of a triangle is A=bh, where b is the base and h is the height. The base of a triangle is always one side length of the parallelogram.
So, if we calculate the area of a triangle with base side length 3 and height 2, we get an area of 6.
Subtracting this from 24 yields an area of 18, so your calculation was correct!
Now you know how to find the area of a parallelogram! Parallelograms are common shapes seen in questions on the GMAT. Knowing how to find their areas will help you in answering those questions.
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