Figure on Same Base and between Same Parallels

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.

Area is measured in m2, cm2, and so on. We also know how to find area of different figure using different formulas. Here we will use the knowledge of these formulas by studying relationship between the areas of the figures when they lie on the same base and between same parallels.

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.

Figure on Same Base


Parallelograms ABCD and EFCD are on the same base DC.

Between the Same Parallels


Triangles ABC and DBC are on the same base BC.


Parallelograms ABCD and triangle EFCD are on the same base DC.

Lie on the Same Base


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.

Figure on Same Base and between Same Parallels








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.

Same Parallels








Solution:

In right angled ∆ ABC, AC = 10 cm and BC = 6 cm. using Pythagoras theorem, we get

AC2 = AB2 + BC2

102 = x2 + 62

⇒ x2 = 102 – 62

⇒ x2 = 100 – 36

⇒ x2 = 64

⇒ 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 ∆BCD

Therefore, area of ∆BCD = 6 × 4 cm2

= 24 cm2

Figure on Same Base and between Same Parallels

Parallelograms on Same Base and between Same Parallels

Parallelograms and Rectangles on Same Base and between Same Parallels

Triangle and Parallelogram on Same Base and between Same Parallels

Triangle on Same Base and between Same Parallels





8th Grade Math Practice

From Figure on Same Base and between Same Parallels to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Multiplication of a Number by a 3-Digit Number |3-Digit Multiplication

    Mar 28, 24 06:33 PM

    Multiplying by 3-Digit Number
    In multiplication of a number by a 3-digit number are explained here step by step. Consider the following examples on multiplication of a number by a 3-digit number: 1. Find the product of 36 × 137

    Read More

  2. Multiply a Number by a 2-Digit Number | Multiplying 2-Digit by 2-Digit

    Mar 27, 24 05:21 PM

    Multiply 2-Digit Numbers by a 2-Digit Numbers
    How to multiply a number by a 2-digit number? We shall revise here to multiply 2-digit and 3-digit numbers by a 2-digit number (multiplier) as well as learn another procedure for the multiplication of…

    Read More

  3. Multiplication by 1-digit Number | Multiplying 1-Digit by 4-Digit

    Mar 26, 24 04:14 PM

    Multiplication by 1-digit Number
    How to Multiply by a 1-Digit Number We will learn how to multiply any number by a one-digit number. Multiply 2154 and 4. Solution: Step I: Arrange the numbers vertically. Step II: First multiply the d…

    Read More

  4. Multiplying 3-Digit Number by 1-Digit Number | Three-Digit Multiplicat

    Mar 25, 24 05:36 PM

    Multiplying 3-Digit Number by 1-Digit Number
    Here we will learn multiplying 3-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. 1. Multiply 201 by 3 Step I: Arrange the numb…

    Read More

  5. Multiplying 2-Digit Number by 1-Digit Number | Multiply Two-Digit Numb

    Mar 25, 24 04:18 PM

    Multiplying 2-Digit Number by 1-Digit Number
    Here we will learn multiplying 2-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. Examples of multiplying 2-digit number by

    Read More

Worksheet on Same Base and Same Parallels