Exploring Area Formulas for Polygons and Triangles

This video tutorial by Kirk Weiler covers the area of polygons, focusing on measurement and modeling. It begins with an introduction to the concept of area, explaining how it differs from perimeter and circumference. The video includes exercises on calculating the area of rectangles, isosceles triangles, and parallelograms, using both basic formulas and more advanced geometric tools like the Pythagorean theorem and trigonometric ratios. The tutorial emphasizes understanding the geometric principles behind area calculations and concludes with a review of key concepts.

What does the area of a shape measure?

• The length around the shape

• The space inside the shape

• The distance across the shape

• The number of edges

How is the area of a rectangle calculated?

• Length divided by width

• Length plus width

• Length times width

• Width minus length

What is the area formula for a parallelogram?

• Base plus height

• Base minus height

• Base times height

• Half of base times height

Why can't the side length of 22 feet be used as the height in the isosceles triangle area calculation?

• It is the base itself

• It is too long

• It is not perpendicular to the base

• It is parallel to the base

How do you find the height of an isosceles triangle for area calculation?

• Multiplying the base by two

• Using the cosine function

• Using the sine function

• Dividing the base by two

What trigonometric function is used to find the base length in the isosceles triangle problem?

• Tangent

• Cosine

• Sine

• Cotangent

What is the area of parallelogram ABCD on the coordinate grid?

• 62 square units

• 82 square units

• 92 square units

• 72 square units

Which side is longer, AB or BC, in the parallelogram on the coordinate grid?

• AB is longer

• BC is longer

• Both are equal

• Cannot be determined

What is the correct expression for the height of the isosceles triangle using trigonometry?

• 10 times the sine of 23 degrees

• 10 times the cosine of 23 degrees

• 10 divided by the sine of 23 degrees

• 10 divided by the cosine of 23 degrees

How is the area of an isosceles triangle calculated using the base and height?

• Base times height divided by two

• Base plus height divided by two

• Base divided by height times two

• Base minus height divided by two