
How do you find the area of a Parallelogram without the height?
Answer
472.5k+ views
Hint: Here, we will use the Trigonometric Ratio of sine to find the height of the triangle, and by using the area of the triangle we will find the area of the congruent triangle in a Parallelogram. By using the area of the congruent triangles, we will find the area of the Parallelogram.
Formula Used:
We will use the following formula:
1. Area of a triangle is given by the formula sq. units
2. Trigonometric Ratio:
Complete Step by Step Solution:
We will find the area of the Parallelogram without the height.
Let ABCD be a Parallelogram. Let be the sides of the Parallelogram and be the height of the Parallelogram.
We are given that the height is unknown. Now, we will find the height of the Parallelogram by using the Area of the Triangle.
Now, we will find the height of the parallelogram by using the area of the triangles.
Trigonometric Ratio:
Now, by using trigonometric ratio in the right angle triangle, we get
By substituting the known values, we get
Multiplying on both sides, we get
Substituting the height and base in the area of the triangle, we get
Area of the Triangle sq. units
We know that the diagonal of a Parallelogram divides the Parallelogram into two congruent triangles. Thus, the Area of the Parallelogram is twice the area of the triangle. Thus, we get
Area of the Parallelogram Area of the Triangle sq. units
Now, by substituting the area of the triangle, we get
Area of the Parallelogram sq. units
Multiplying the terms, we get
Area of the Parallelogram sq. units
Therefore, the area of the Parallelogram is sq. units when the height is unknown.
Note:
We know that the Area of a Parallelogram is the region occupied by a Parallelogram in a two- dimensional Plane. We can also find the area of the Parallelogram by using the area of the Parallelogram even though height is not unknown.
We know that Area of a Parallelogram sq. units
Substituting the height and base in the area of the triangle, we get
Area of a Parallelogram sq. units
Therefore, the area of the Parallelogram is sq. units when the height is unknown.
Formula Used:
We will use the following formula:
1. Area of a triangle is given by the formula
2. Trigonometric Ratio:
Complete Step by Step Solution:
We will find the area of the Parallelogram without the height.

Let ABCD be a Parallelogram. Let
We are given that the height is unknown. Now, we will find the height of the Parallelogram by using the Area of the Triangle.
Now, we will find the height of the parallelogram by using the area of the triangles.
Trigonometric Ratio:
Now, by using trigonometric ratio in the right angle triangle, we get
By substituting the known values, we get
Multiplying
Substituting the height and base in the area of the triangle, we get
Area of the Triangle
We know that the diagonal of a Parallelogram divides the Parallelogram into two congruent triangles. Thus, the Area of the Parallelogram is twice the area of the triangle. Thus, we get
Now, by substituting the area of the triangle, we get
Multiplying the terms, we get
Therefore, the area of the Parallelogram is
Note:
We know that the Area of a Parallelogram is the region occupied by a Parallelogram in a two- dimensional Plane. We can also find the area of the Parallelogram by using the area of the Parallelogram even though height is not unknown.
We know that Area of a Parallelogram
Substituting the height and base in the area of the triangle, we get
Therefore, the area of the Parallelogram is
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