Parallelogram: Same base, Same height
Theorem: Parallelograms standing on the same base and between the same parallel lines are equal in area.
In the figure below, the two parallelograms ▱ ABCD and ▱ ABDE are identical in width (because the base AB is same). Also these two parallelograms ▱ ABCD and ▱ ABDE are between the same parallel lines AB||DC, so they are also identical in height. In geometry, the area of any parallelogram is just \(\text{base} \times \text{height}\) . Since both have the same base and the same height, their "insides" (area) is exactly the same, even if one looks more tilted than the other!
एउटै आधार र उही समानान्तर रेखाहरू बीच रहेका समानान्तर चतुर्भुजहरूको क्षेत्रफल बराबर हुन्छ ।
तलको चित्रमा, दुईवटा समानान्तर चतुर्भुजहरू ▱ ABCD र ▱ ABDE को चौडाइ समान छ (किनभने आधार AB एउटै छ)। साथै, ति समानान्तर चतुर्भुजहरू ▱ ABCD र ▱ ABDE उही समानान्तर रेखाहरू AB||DC बीच रहेका छन्, त्यसैले तिनीहरूको उचाइ पनि समान छ। ज्यामितिमा, कुनै पनि समानान्तर चतुर्भुजको क्षेत्रफल भन्नाले आधार x उचाइ हुन्छ । दुवैको आधार र उचाइ एउटै भएकाले, एउटा अर्कोभन्दा बढी ढल्केको देखिए तापनि तिनीहरूको "भित्री भाग" (क्षेत्रफल) रूपमा बराबर हुन्छ !
In the figure below, the two parallelograms ▱ ABCD and ▱ ABDE are identical in width (because the base AB is same). Also these two parallelograms ▱ ABCD and ▱ ABDE are between the same parallel lines AB||DC, so they are also identical in height. In geometry, the area of any parallelogram is just \(\text{base} \times \text{height}\) . Since both have the same base and the same height, their "insides" (area) is exactly the same, even if one looks more tilted than the other!
एउटै आधार र उही समानान्तर रेखाहरू बीच रहेका समानान्तर चतुर्भुजहरूको क्षेत्रफल बराबर हुन्छ ।
तलको चित्रमा, दुईवटा समानान्तर चतुर्भुजहरू ▱ ABCD र ▱ ABDE को चौडाइ समान छ (किनभने आधार AB एउटै छ)। साथै, ति समानान्तर चतुर्भुजहरू ▱ ABCD र ▱ ABDE उही समानान्तर रेखाहरू AB||DC बीच रहेका छन्, त्यसैले तिनीहरूको उचाइ पनि समान छ। ज्यामितिमा, कुनै पनि समानान्तर चतुर्भुजको क्षेत्रफल भन्नाले आधार x उचाइ हुन्छ । दुवैको आधार र उचाइ एउटै भएकाले, एउटा अर्कोभन्दा बढी ढल्केको देखिए तापनि तिनीहरूको "भित्री भाग" (क्षेत्रफल) रूपमा बराबर हुन्छ !
To find its area of parallelogram, we use the formula
\(\square= bh\)
Here, the base is b, and the height h is the perpendicular distance from the base to the opposite vertex.
समानान्तर चतुर्भुजको क्षेत्रफल पत्ता लगाउन हामी तलको सूत्र प्रयोग गर्छौं:
\(\square = bh\)
यहाँ, \(b\) आधार हो, र उचाइ \(h\) भनेको आधारदेखि विपरीत शीर्षबिन्दु (vertex) सम्मको लम्ब दूरी (perpendicular distance) हो ।
\(\square= bh\)
Here, the base is b, and the height h is the perpendicular distance from the base to the opposite vertex.
समानान्तर चतुर्भुजको क्षेत्रफल पत्ता लगाउन हामी तलको सूत्र प्रयोग गर्छौं:
\(\square = bh\)
यहाँ, \(b\) आधार हो, र उचाइ \(h\) भनेको आधारदेखि विपरीत शीर्षबिन्दु (vertex) सम्मको लम्ब दूरी (perpendicular distance) हो ।
Try it: Drag A or B or D
तलको चित्रमा बिन्दुहरु A वा B वा D लाई तल माथी दाँया बाँया चलाएर ▱ ABCD र ▱ ABDE को क्षेत्रफल बारे जानकारी लिनुहोस। NOTE: Drag the points A or B or D.Based on the figure, Play Quiz 1
After adjusting the parallelogram (if desired), answer the questions below based on the abovefigure. All numerical answers should be to one decimal place.- What is the length (base) of ▱ ABCD?
- What is the height of ▱ ABCD?
- What is the length (base) of ▱ ABDE?
- What is the height of ▱ ABDE?
- What is the area of ▱ ABCD?
- What is the area of ▱ ABDE?
- What is the relation between the areas of ▱ ABCD and ▱ ABDE?
Next model and next Updates are coming soon!
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