Category :
9th Class
Areas of Parallelograms and Triangles
- A polygonal region is the union of a polygon and it’s interior. For e.g., the union of a triangle and its interior is called the triangular region.
- Every polygonal region has area. Area of a figure is a number associated with the part of the plane enclosed by that figure.
- Two congruent figures have equal areas but figures with equal areas need not be congruent.
- If ABCD is a rectangle with AB = \[l\] m and BC = b m, then the area of the rectangular region ABCD is\[lb\text{ }sq.\text{ }m\text{ }or\text{ l}b\text{ }{{m}^{2}}\].
- If A and B are two regions having at the most a line segment common between them two, then the area of their combined region S is equal to the sum of their areas taken separately. i.e, ar (S) = ar (A) +ar (B).
- The area of a parallelogram is the product of any of its sides and the corresponding altitude.
- Two figures are said to be on the same base and between the same parallels, if they have a common base (side) and the vertices, (or the vertex) opposite to the common base of each figure lie on the same line parallel to the base.
- A diagonal of a parallelogram divides it into two triangles of equal areas.
- Parallelograms on the same (or equal) base and between the same parallel lines are equal in area.
- Parallelograms on the same base (or equal bases) and having equal areas lie between the same parallels.
- Parallelograms on equal bases and between the same parallel lines are equal in area.
- Area of a triangle is half the product of any of its sides and the corresponding altitude.
- Triangles on the same base and between the same parallel lines are equal in area.
- Two triangles having the same base (or equal bases) and equal areas lie between the same parallel lines.
- If a triangle and a parallelogram are on the same base and between the same parallel lines, then the area of the triangle is equal to half that of the parallelogram.
- The area of a trapezium is half the product of its height and the sum of the parallel sides.
- Triangles with equal areas and having one side of one triangle, equal to one side of the other, have their corresponding altitudes equal.
- A rectangle and a parallelogram on the same base and between the same parallels have the same area.
- A median of a triangle divides it into two triangles of equal area.
