Here we will learn about the
figure on same base and between same parallels. We know the measure of the
plane region enclose by a closed figure is called its area.
Two geometric figures are said to be on the same base and between the same parallels, if they have a common side as base and vertices opposite to the common base lie on the line parallel to the base.
Trapezium ABCD and parallelogram EFCD have a common side DC. We say that trapezium ABCD and parallelogram EFCD are on the same base DC.
Parallelograms ABCD and EFCD are on the same base DC.
Triangles ABC and DBC are on the same base BC.
Parallelograms ABCD and triangle EFCD are on the same base DC.
Solved example for the figure on same base and between same parallels:
1. Here ∆ABC and ∆DBC have the same base BC and are between the same parallel ‘p’ and BC.
Base and altitude of the figure
Base: Any side of the figure is called the base.
Altitude: A line segment joining the vertex and perpendicular to the opposite side is called the altitude.
2. ABC is right angled at B with BC = 6 cm and AC = 10 cm. also ∆ABC and ∆BCD are on the same base BC. Find the area of ∆BCD.
In right angled ∆ ABC, AC = 10 cm and BC = 6 cm. using Pythagoras theorem, we getAC2 = AB2 + BC2
⇒ x = √64
⇒ x = √(8 × 8)
⇒ x = 8 cm
Now, since ∆ ABC and ∆BCD are on the same base BC.
Therefore, area of ∆ ABC = Area of ∆BCD
⇒ 1/2 × base × height = Area of ∆BCD
⇒ 1/2 × 6 × 8 = Area of ∆BCDTherefore, area of ∆BCD = 6 × 4 cm2