A. A parallelogram has a base of 3.5 units and a...

a. A parallelogram has a base of $3.5$ units and a corresponding height of 2 units. What is its area? b. A parallelogram has a base of 3 units and an area of $1.8$ square units. What is the corresponding height for that base? c. A parallelogram has an area of $20.4$ square units. If the height that corresponds to a base is 4 units, what is the base?

a. A parallelogram has a base of $3.5$ units and a corresponding height of 2 units. What is its area?
b. A parallelogram has a base of 3 units and an area of $1.8$ square units. What is the corresponding height for that base?
c. A parallelogram has an area of $20.4$ square units. If the height that corresponds to a base is 4 units, what is the base?

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Key Concepts

Area of a Parallelogram

The area of a parallelogram is calculated by multiplying the length of its base by the corresponding height (the perpendicular distance from the base to the opposite side). This concept is central to understanding how to determine the size of two-dimensional figures such as parallelograms.

Base

In the context of a parallelogram, the base is one of its sides chosen for the purpose of calculating the area. It is important to note that the base must have a corresponding height measured at a right angle to it to apply the area formula correctly.

Height

The height (or altitude) of a parallelogram is the perpendicular distance from the chosen base to the opposite side. This concept is crucial because the area calculation depends strictly on this perpendicular measurement, not on the length of the slanted sides.

Algebraic Manipulation

Algebraic manipulation is often employed to rearrange the area formula of a parallelogram to solve for the unknown variable when given the area along with either the base or the height. This technique is fundamental in geometric problem solving.

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