Parallelograms are quadrilaterals with opposite sides of equal length and parallel sides. The area of a parallelogram is determined by the number of rows of parallelogram shapes it has and the size of those shapes.
Parallelograms can be oriented in different directions. The area of a parallelogram depends on how you measure it. For example, if you measure the area of a vertical parallelogram by measuring the width and length, then you would get a different answer than if you measured the area by measuring the length and height.
This problem asks you to find the area of a parallelogram with given vertices (corners). First, you must identify whether or not the parallelogram is oriented in a certain direction. Then, you must identify all of its vertices and calculate the area using that information.
Find the base and height of the triangle ABC
The base of the parallelogram is found by finding the average of the two bases of the adjacent triangles. The average of the two bases is found by multiplying them together and dividing by two.
The height of the parallelogram is simply the length of one side of any given vertex. In this problem, the height is simply the length of any side of vertex B.
Parallelograms have two kinds of angles: rhombus angles and rectangle angles. Rhombus angles are those that are not equal to ninety degrees (º); rectangle angles are those that are ninety degrees (º).
In this problem, all four corners are rhombus corners, so to find the area you must divide the base times one half times the perpendicular height.
Calculate the area of triangle ABC
The area of triangle ABC is made up of the area of the rectangle with length 4 and height 3, plus the area of the triangle with base length 1 and height 4.
You can see this in the diagram above, where we have labeled these areas A1 and A2, respectively. Since there are two rectangles and one triangle, we can add these together to get the total area of ABC: A1 + A2 = 6 + 2 = 8.
Now that we have found the area of triangle ABC, we can go back to finding the area of parallelogram ABDE. We know that one side is 8 units long, so we can find the length of each of its four corners by multiplying 8 by −3, −1, 6, and 4, respectively. Then we can find the area by drawing square bases on each corner and filling in the space with unit squares.
Calculate the area of rectangle ABDC
The next step is to calculate the area of the rectangle that lies between points A and D, and DC. To do this, you need to calculate the area of the rectangle that lies between points A and C, and DC.
Then, you need to add the area of rectangle ABDC to the area of rectangle ACDC. You do this because ABDC overlaps ACDC by half of its length and width.
Area of Rectangle ABDC=Base√2×Height=AB√2×0=AB×0=0 Area of Rectangle ACDC=Base√2×Height=AC√2×3=AC√6×3=18 Square units Total Area=ABDC+ACDC 18+18 36 square units
The answer is 36 square units.
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Created: September 6, 2010 … Updated: February 13, 2019 …
Use algebra to find the area
Now that you have the vertices of your parallelogram, you can use algebra to find the area. The area of a parallelogram is found by subtracting the sum of the opposite sides from the length of the opposite side with the greatest length.
So, let’s start by finding the length of side AB. We know that AB = 6 + (−1) = 5 Therefore, our final answer will be:
Area = ½ × (5) × (6) × (3) = ½ × 30 = 15 This is the area of one side of the parallelogram. To find the total area, we need to multiply this by 4, since there are 4 sides. The total area is 60 square units.
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