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Perimeter and Area - Area of a Parallelogram

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A parallelogram is a quadrilateral where opposite sides are parallel and equal in length. Any side of the parallelogram can be considered its base.

A parallelogram with labels showing the base and parallel sides.
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The height (or altitude) of a parallelogram is the perpendicular distance from the base to the opposite side. It must be at a 90∘90^{\circ} angle to the base.

Parallelogram showing the perpendicular height dropped from a vertex to the base.
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The area of a parallelogram is calculated as the product of its base (bb) and its corresponding height (hh). If you cut a right-angled triangle from one side and move it to the other, the parallelogram becomes a rectangle of the same area.

A rectangle illustrating that the area formula is the same as a parallelogram's.
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If the area and one dimension (base or height) are known, the other dimension can be found by dividing the area by the known dimension.

📐Formulae

Area of a Parallelogram=b×h\text{Area of a Parallelogram} = b \times h

Base (b)=AreaHeight\text{Base (b)} = \frac{\text{Area}}{\text{Height}} strength

Height (h)=AreaBase\text{Height (h)} = \frac{\text{Area}}{\text{Base}}

💡Examples

Problem 1:

Find the area of a parallelogram whose base is 12 cm12\text{ cm} and corresponding height is 7 cm7\text{ cm}.

Solution:

Given:\nBase (bb) = 12 cm12\text{ cm}\nHeight (hh) = 7 cm7\text{ cm}

Using the formula: Area=b×h\text{Area} = b \times h Area=12 cm×7 cm\text{Area} = 12\text{ cm} \times 7\text{ cm} Area=84 cm2\text{Area} = 84\text{ cm}^{2}

Explanation:

To find the area, we simply identify the base and the perpendicular height from the problem and multiply them together. Ensure the units are square centimeters.

Problem 2:

The area of a parallelogram is 48 cm248\text{ cm}^{2} and its height is 6 cm6\text{ cm}. Find the length of its base.

Solution:

Given:\nArea = 48 cm248\text{ cm}^{2}\nHeight (hh) = 6 cm6\text{ cm}

Using the formula for base: Base (b)=AreaHeight\text{Base (b)} = \frac{\text{Area}}{\text{Height}} Base (b)=486\text{Base (b)} = \frac{48}{6} Base (b)=8 cm\text{Base (b)} = 8\text{ cm}

Explanation:

When the area and height are known, we can find the missing base by dividing the total area by the given height.

Problem 3:

Find the area of the parallelogram ABCDABCD where the base BC=8 cmBC = 8\text{ cm} and the altitude AMAM drawn to the base BCBC is 5.5 cm5.5\text{ cm}.

Parallelogram ABCD with base 8cm and height 5.5cm.

Solution:

Given: Base (bb) = 8 cm8\text{ cm} Height (hh) = 5.5 cm5.5\text{ cm}

Using the formula: Area=b×h\text{Area} = b \times h Area=8×5.5\text{Area} = 8 \times 5.5 Area=44 cm2\text{Area} = 44\text{ cm}^{2}

Therefore, the area of the parallelogram is 44 cm244\text{ cm}^{2}.

Explanation:

Identify the base and the corresponding perpendicular height. Multiply the two values together to find the total surface area in square units.

Problem 4:

One side of a parallelogram is 15 cm15\text{ cm} and the area is 120 cm2120\text{ cm}^{2}. Find the distance between the side and the opposite side.

Parallelogram with area 120 and base 15, height labeled as unknown.

Solution:

Given: Area = 120 cm2120\text{ cm}^{2} Base (bb) = 15 cm15\text{ cm} Distance between sides (Height hh) = ?

Using the formula: h=Areabh = \frac{\text{Area}}{b} h=12015h = \frac{120}{15} h=8 cmh = 8\text{ cm}

So, the height of the parallelogram is 8 cm8\text{ cm}.

Explanation:

The distance between two parallel sides is the perpendicular height. To find the height, divide the given area by the base length.