Area of Parallelograms: Area of a parallelogram is caluculated as the product of base and the corresponding height.
In the figure ABCD is a parallelogram where AL CD and CM AD. To calculate area of this parallelogrami if we consider the base as CD then the corresponding height will be AL because AL CD, but if we take base as AD then the corresponding height will be CM because CM AD. Thus Area of parallelogram ABCD = Base X height = AD X CM = CD X AL
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Theorem 1 The area of a parallelogram is the product of its base and the corresponding altitude.
Given A parallelogram ABCD in which AB is the base and AL the corresponding altitude. To prove Construction Draw BM produced DC to M. Now is a rectangle. Proof Since and rectangle are on the same base and between the same parallels.
[ The area of Rectangle = Base X Height ] Hence, |
Illustration: I n the given figure, ABCD is a parallelogram, AL ⊥ DC and CM ⊥ AD. If AB = 14 cm. AL = 10 cm and CM = 7 cm, find AD.
Area of paralleogram ABCD = DC × AL (Taking base as DC and Height as AL ) Area of paralleogram ABCD = AB × AL (AB = DC as opposite side of the parallelogram are equal) Therefore, Area of paralleogram ABCD = 14 × 10 ……(1) Taking the base of Parallelogram ABCD as AD the height will be CM Area of paralleogram ABCD = AD × CM (taking base as AD and height as CM) Area of paralleogram ABCD = AD × 7 ……(2) Since equation 1 and 2 both represent the Area of the same Parallelogram ABCD , both should be equal. Hence from equation (1) and (2), This means that, 14 X 10 = AD X 7 AD X 7 = 14 X 10
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ABCD and PQRS are two parallelograms with equal areas and AB=PQ. Which of the following relations is true?
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Right Option : C | |||
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Find the area of the parallelogram with the base of 4 cm and height of 5 cm. | |||
Right Option : B | |||
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The area of a parallelogram is 500 sq.cm. Its height is twice its base. Find the height and base. | |||
Right Option : A | |||
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