1. Area of a Parallelogram
A parallelogram is a quadrilateral where both pairs of opposite sides are parallel and equal. Unlike rectangles, the angles of a parallelogram do not have to be right angles.
The area of a parallelogram tells us how much surface it covers. Even though a parallelogram may look slanted, its area is still calculated using the base and the perpendicular height.
1.1. Base and Height in a Parallelogram
The base (b) is any side of the parallelogram chosen to measure the area. The height (h) is the perpendicular distance from the opposite side to the base.
Note that height is not the slanted side length. It must be measured as a right-angle distance.
2. Area Formula
The formula for the area of a parallelogram is:
\( A = b \times h \)
where:
- \(b\) = base
- \(h\) = height (perpendicular to the base)
2.1. Why the Formula Works
A parallelogram can be thought of as a slanted rectangle. If we cut a right triangle from one side and shift it to the other side, the shape becomes a rectangle with:
- the same base \(b\)
- the same height \(h\)
And since the area of a rectangle is \( b \times h \), the same formula works for a parallelogram.
3. Examples
Let’s apply the formula to understand it better.
3.1. Example 1
A parallelogram has a base \(b = 14\,\text{cm}\) and height \(h = 8\,\text{cm}\). The area is:
\( A = b \times h = 14 \times 8 = 112\,\text{cm}^2 \)
3.2. Example 2
A parallelogram-shaped field has a base \(b = 50\,\text{m}\) and corresponding height \(h = 30\,\text{m}\). The area covered is:
\( A = 50 \times 30 = 1500\,\text{m}^2 \)