Calculating Areas of Shapes

The video tutorial covers geometry concepts for sixth graders, focusing on decomposing figures to find areas. It begins with a wood lot problem, calculating lengths of line segments, and progresses to finding areas of rectangles, parallelograms, and trapezoids using different decomposition methods. The tutorial emphasizes that different strategies can yield the same area results.

If AB is 10 units, FE is 8 units, and AF is 6 units, what is the length of BC?

• 10 units

• 13 units

• 15 units

• 8 units

Given DC is 10 units, FE is 30 units, and AF is 28 units, what is the length of AB?

• 36 units

• 42 units

• 38 units

• 40 units

How can you decompose a figure into rectangles to find its area?

• Using only vertical lines

• Using only horizontal lines

• Using diagonal lines

• Using both horizontal and vertical lines

What is the area of a rectangle with a base of 2m and a height of 4m?

• 6 m²

• 8 m²

• 10 m²

• 12 m²

When viewing a figure as a large rectangle with a piece removed, what operation is needed to find the area of the original figure?

• Division

• Subtraction

• Multiplication

• Addition

What is the area of a large rectangle with dimensions 7m by 9m?

• 72 m²

• 81 m²

• 63 m²

• 54 m²

How do you find the area of a triangle with a base of 6m and a height of 4m?

• Multiply base and height

• Multiply base and height, then divide by 2

• Add base and height

• Subtract base from height

What is the area of a triangle with a base of 8m and a height of 5m?

• 20 m²

• 30 m²

• 40 m²

• 20 m²

What is the area of a trapezoid if the areas of its two triangles are 20 m² and 10 m²?

• 40 m²

• 25 m²

• 30 m²

• 35 m²

Why does the area remain the same regardless of how a figure is decomposed?

• Because the perimeter is constant

• Because the base and height are fixed

• Because the angles are equal

• Because the total area is independent of decomposition