Area of Parallelograms
Area of Parallelograms
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 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 Proof Since
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 | |
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 | |||
| View Explanation | |||
Find the area of the parallelogram with the base of 4 cm and height of 5 cm. | |||
| Right Option : B | |||
| View Explanation | |||
The area of a parallelogram is 500 sq.cm. Its height is twice its base. Find the height and base. | |||
| Right Option : A | |||
| View Explanation | |||
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