- Step IV: Paste the triangular portion (PSE) on the white chart joining sides RQ and SP.Īfter doing this activity, we observed that the area of a rectangle is equal to the area of a parallelogram.
- Step III: Paste the remaining portion (EQRS) on a white chart.
- Step II: Cut the triangular portion (PSE).
- Step I: Draw a parallelogram (PQRS) with altitude (SE) on a cardboard and cut it.
- Let's do an activity to understand the area of a parallelogram. Thus, the area of the given parallelogram is base times the altitude. Using grid paper, let us find its area by counting the squares.Īrea = 16 + (1/2) × 8 = 16 + 4 = 20 unit 2Īlso, we observe in the figure that ST ⊥ PQ. Let us analyze the above formula using an example. The formula to calculate the area of a parallelogram can thus be given as,Īrea of parallelogram = b × h square units The base and altitude of a parallelogram are perpendicular to each other as shown in the following figure. For now, we will just use this as a fact.The area of a parallelogram can be calculated by multiplying its base with the altitude. You can see this most easily when you draw a parallelogram on graph paper or look at the diagram below. In high school, you will be able to prove that a perpendicular segment from a point on one side of a parallelogram to the opposite side will always have the same length.
This is so that we don’t get confused about whether × means multiply, or whether the letter x is standing in for a number. Notice that the multiplication symbol can be written with a small dot instead of a × symbol.
If b is base of a parallelogram (in units), and h is the corresponding height (in units), then the area of the parallelogram (in square units) is the product of these two numbers b Even though the two rectangles have different side lengths, the products of the side lengths are equal, so they have the same area! And both rectangles have the same area as the parallelogram. Notice that the side lengths of each rectangle are the base and height of the parallelogram. There are infinitely many line segments that can represent the height! If we draw any perpendicular segment from a point on the base to the opposite side of the parallelogram, that segment will always have the same length.Both the side (the segment) and its length (the measurement) are called the base. We can choose any of the four sides of a parallelogram as the base.If both the height and base were 100 times the original the area would be 100 × 100 = 10000 times the original area. If both the height and base tripled, the area would be 3 × 3 = 9 times the original area. Hence, if a given height h and a given base b are doubled the result would be 2 b × 2 h = 4 A, where A was the original area. If the height is 100 times the original, the area would be 100 times the original. If the height triples, the area would triple. Hence, if a given height h doubles the result would be b × 2 h = 2 A, where A was the original area.