Triangle and Parallelogram on Same Base and between Same Parallels

Triangle and parallelogram on same base and between same parallels.

If a triangle and a parallelogram are on the same base and between the same parallels, then the area of triangle is equal to half the area of the parallelogram.

In the adjoining figure, parallelogram ABCD and ∆ABD are on the same base AB and between the same parallels AF and DC.

Triangle and Parallelogram on Same Base and between Same Parallels






Therefore, area of ∆ABD = 1/2 area of parallelogram ABCD

                                  = 1/2 (AB × AE);

                                      [Since, DE is the altitude of parallelogram ABCD]

Here, AB is the base and AE is the height of ∆ABD.

Notes:

1. If a triangle and parallelogram are on the same base and have the same altitude, the area of the triangle will be half that of the parallelogram.

If they have same altitude, they will lie between the same parallels. Hence the area of the triangle will be equal to half that of the parallelogram.

2. If a triangle and a rectangle be on the same base and between the same parallels, the area of the triangle will be half that of the rectangle.

3. Area of a triangle = 1/2 × base × altitude.

∆ ABC and rectangle BCDE are on the same base BC and between the same parallels BC and ED.

Same Base and between Same Parallels







Therefore, ∆ ABC = 1/2 rectangle BCDE = 1/2 BC ∙ CD

                        = 1/2 BC ∙ AP [Since APCD is a rectangle]



Solved example for the triangle and parallelogram on same base and between same parallels:

1. ∆ ABD and parallelogram ABCD are on the same base AB. If base and altitude of the parallelogram are 15 cm and 10 cm, find the area of the triangle.

Solution:            

Base of parallelogram = 15 cm

Altitude of parallelogram = 10 cm

Triangle and Parallelogram on Same Base






Therefore Area of parallelogram = 15 × 10 cm2

                                            = 150 cm2

∆ ABD and parallelogram ABCD are on the same base AB.

Therefore of ∆ ABD = 1/2 the area of parallelogram ABCD

                           = 1/2 × 150 cm2

                           = 75 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 Triangle and Parallelogram on Same Base and between Same Parallels to HOME PAGE




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.



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.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 25, 25 12:21 PM

    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  2. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  3. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  4. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 23, 25 11:37 AM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More

  5. 5th Grade Volume | Units of Volume | Measurement of Volume|Cubic Units

    Jul 20, 25 10:22 AM

    Cubes in Cuboid
    Volume is the amount of space enclosed by an object or shape, how much 3-dimensional space (length, height, and width) it occupies. A flat shape like triangle, square and rectangle occupies surface on…

    Read More

Worksheet on Same Base and Same Parallels