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Example: The angle between any two sides of a parallelogram is 90 degrees. If the length of the two adjacent sides are 3 cm and 4 cm, respectively, then find the area. Solution: Let a = 3 cm and b=4 cm. x = 90 degrees. Area = ab sin (x) A = 3 × 4 sin (90) A = 12 sin 90. A = 12 × 1 = 12 sq.cm.
- Area and Perimeter
The perimeter of an equilateral triangle is 21cm. Find its...
- Area of Square
Area of a square is defined as the number of square units...
- Area of Hollow Cylinder
Example: Find (in cm 2) the curved surface area of a hollow...
- Area and Perimeter
Using the formula for the area of a parallelogram with adjacent sides and the angle between them: Area = a × b × sin (θ) Area = 5 × 8 × sin (60º) Area = 40 × 3 2. Area = 20 3 square units. Therefore, the area of the parallelogram is 20 3 square units. Finding Area of Parallelogram Using Diagonals.
- Can any side of a parallelogram be considered as the base?Yes, any of the parallel sides can be chosen as the base.
- How is the height of a parallelogram measured?The height is the perpendicular distance between the base and the opposite parallel side.
- What happens to the area of a parallelogram if the base is doubled?If the base of a parallelogram is doubled while the height remains the same, the area will also be doubled.
- How is the area of a parallelogram affected if the height is halved?If the height of a parallelogram is halved while the base remains the same, the area will be halved.
- With Base and Height
- Without Height
- Using Diagonals
- In Vector Form
The formula to calculate the area of a parallelogram when base and height are known is given below: Derivation with Example To understand why the above formula is b × h, convert a parallelogram with base (b) and height (h), into a rectangle as shown in the figure below. After you convert the parallelogram into a rectangle 1. The base of the paralle...
When we don’t know the height of the parallelogram, we use trigonometry to find its area. We will calculate the area of a parallelogram (A) using its adjacent sides and the angle between the sides. Derivation ∵ We don’t know the height of a parallelogram, we take an imaginary height that is just opposite the angle x. From trigonometry concept, we k...
Here we will learn how to calculate the area of a parallelogram when the 2 diagonals are given along with its angle of intersection. Note:x + y = 180, since diagonals are straight lines ∴ y = 180 – x Also, sin(x) = sin(180 -x) So the formula above is justified Let us solve an example:
There are two ways to calculate the area of a parallelogram in vector form. The formulas are given below:
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- 16 min
- Parallelogram Definition. A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure.
- Shape of Parellelogram. A parallelogram is a two-dimensional shape. It has four sides, in which two pairs of sides are parallel. Also, the parallel sides are equal in length.
- Special Parallelograms. Square and Rectangle: A square and a rectangle are two shapes which have similar properties to a parallelogram. Both have their opposite sides equal and parallel to each other.
- Angles of Parallelogram. A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees.
The formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle. But wait! Why are the formulas the same? Look what happens when we slide part of the parallelogram to the right. Genius! We made the parallelogram into a rectangle. Key intuition: We can make every parallelogram into a rectangle ...
The formula is given as, area = ½ × d 1 × d 2 sin (x), where 'd1' and 'd2' are lengths of diagonals of the parallelogram, and 'x' is the angle between them. Area of a parallelogram is defined as the region covered by a parallelogram in a two-dimensional plane and is expressed in square units. It is found by the formula base times height.
Example 1: decompose the parallelogram. Decompose the parallelogram and rearrange its part so that they form a rectangle. Then find the area. Decompose the parallelogram into two triangles and a rectangle. 2 Move one triangle to the opposite side of the parallelogram so that the shape is now a rectangle.
