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.
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.
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
= 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.
Recent Articles
-
Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns
Dec 13, 24 08:43 AM
We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r… -
Patterns in Math | Missing Number | Counting Numbers | Worksheets
Dec 13, 24 12:31 AM
Finding patterns in math is very important to understand the sequence in the series. We need to find the exact missing number that from the group of numbers. The counting numbers may be counting -
Concept of Pattern | Similar Patterns in Mathematics | Similar Pattern
Dec 12, 24 11:22 PM
Concept of pattern will help us to learn the basic number patterns and table patterns. Animals such as all cows, all lions, all dogs and all other animals have dissimilar features. All mangoes have si… -
2nd Grade Geometry Worksheet | Plane and Solid Shapes | Point | Line
Dec 12, 24 10:31 PM
2nd grade geometry worksheet -
Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical
Dec 09, 24 10:39 PM
What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver…
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.