Understanding the Area of a Parallelogram

The video tutorial explains how to find the area of a parallelogram. It begins by defining a parallelogram as a quadrilateral with opposite sides that are parallel and congruent. The tutorial then demonstrates how to calculate the area using the formula 'area = base * height', emphasizing the importance of using the correct height, which is the perpendicular distance between the bases. An example is provided with a parallelogram having sides of 8 and 5, and a height of 4, resulting in an area of 32 square units. The tutorial further explores a more complex example involving a 30-60-90 triangle to find the height and area of a parallelogram with sides of 6 and 10, and a 60-degree angle, resulting in an area of 30√3 square units.

What is a defining characteristic of a parallelogram?

• All angles are right angles

• Opposite sides are parallel

• All sides are equal

• It has three sides

To find the area of a parallelogram, you need to multiply the base by which other measurement?

• Height

• Width

• Perimeter

• Diagonal

In the example given, what is the height used to calculate the area of the parallelogram with sides 8 and 5?

• 10

• 5

• 4

• 8

What type of triangle is used in the more complex example involving a parallelogram?

• Equilateral triangle

• Isosceles triangle

• 30-60-90 triangle

• 45-45-90 triangle

In a 30-60-90 triangle, if the hypotenuse is 6, what is the length of the short leg?

• 3

• 6

• 9

• 12

What is the formula for the hypotenuse in a 30-60-90 triangle?

• x/2

• x

• x√3

• 2x

In the complex example, what is the base used for calculating the area of the parallelogram?

• 10

• 6

• 3

• 5

What is the final area of the parallelogram in the complex example?

• 15√3

• 60

• 30√3

• 30

What is the relationship between the short leg and the long leg in a 30-60-90 triangle?

• The long leg is twice the short leg

• The long leg is half the short leg

• The long leg is the same as the short leg

• The long leg is the short leg times √3

What is the unit of measurement for area?

• Cubic units

• Linear units

• Square units

• None of the above