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Calculate the area of parallelograms

Area of a parallelogram measures the amount of two-dimensional space it covers and is calculated as A=b×hA=b\times h, where bb is a chosen base and hh is the perpendicular distance between the parallel sides. Decomposing and rearranging a parallelogram into a rectangle explains why the formula works and clarifies that a slanted side is not the height; answers are expressed in square units using whole-number, decimal, or simple fractional measurements. Coordinate-based and more abstract generalizations are not included.

Detailed Explanation: Calculate the area of parallelograms

The area of a parallelogram is the amount of space inside it. Use the formula

A=b×hA=b\times h

where:

  • bb is the length of the chosen base.
  • hh is the perpendicular height, the straight-up-and-down distance between the parallel sides.

The slanted side is not usually the height. The height must meet the base at a right angle.

Example: Find the area of a parallelogram with a base of 88 cm and a perpendicular height of 55 cm.

  1. Identify the base and height:

b=8 cm,h=5 cmb=8\text{ cm}, \qquad h=5\text{ cm}

  1. Substitute the values into the formula:

A=b×hA=b\times h A=8×5A=8\times5

  1. Multiply:

A=40A=40

  1. Write the answer in square units:

40 cm2\boxed{40\text{ cm}^2}

You can also see why the formula works by cutting off the triangle on one slanted side and moving it to the other side. This makes a rectangle with the same base and height, so its area is still b×hb\times h.

Learn by doing: Calculate the area of parallelograms

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    Area of a Parallelogram - Advanced

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