Exploring Area of Polygons in the Coordinate Plane

The video tutorial provides extra practice on calculating the area and perimeter of polygon shapes in the coordinate plane using three methods: boxing in, the general area formula, and the shoelace formula. The instructor begins with the boxing in method, demonstrating how to find the area by creating a rectangle around the shape and subtracting the areas of right triangles. The general area formula is then introduced, requiring the division of a quadrilateral into triangles and translating points to the origin. Finally, the shoelace formula is presented as a quicker alternative for calculating area without translation or division into triangles.

What is the primary method introduced in the video for finding the area of polygon shapes?

• Shoelace formula

• General area formula

• Pythagorean theorem

• Boxing in method

How do you calculate the area of the shaded region using the 'boxing in' method?

• Add the areas of all triangles

• Subtract the areas of triangles from the rectangle

• Divide the rectangle into smaller rectangles

• Multiply the length and width of the rectangle

What is the result of the area calculation using the 'boxing in' method for the example given?

• 12 square units

• 25 square units

• 13 square units

• 9 square units

How is the area of each triangle calculated in the 'boxing in' method?

• Base divided by height

• Base plus height

• Base times height

• One-half base times height

What is necessary for using the general area formula for triangles?

• The triangle must be right-angled

• One vertex of the triangle must be at the origin

• All vertices must be on the x-axis

• The triangle must have equal sides

What transformation is applied to use the general area formula for triangles?

• Translation

• Rotation

• Scaling

• Reflection

What is the purpose of translating points in the general area formula method?

• To place a vertex at the origin

• All of the above

• To simplify the calculation of the area

• To align points with the coordinate axes

What does the shoelace formula simplify in the process of finding areas?

• Calculating the perimeter

• Subtraction of areas

• Translation of points

• Breaking the shape into triangles

What is the final area found using the shoelace formula for the example?

• 24 square units

• 6 square units

• 12 square units

• 18 square units

Which method does the video claim to be quicker than the others for finding the area?

• Boxing in method

• None of the above

• General area formula

• Shoelace formula