Area and Decomposition of Shapes

The video tutorial covers lesson three on reasoning to find area. It begins with comparing the areas of two figures, A and B, and explains that their areas remain the same despite rearranging parts. The tutorial then demonstrates how to calculate area using decomposition on a grid, focusing on rearranging and adding smaller areas. It progresses to more complex shapes, using triangles to find shaded areas, and concludes with calculating areas of shapes not aligned to a grid. The key concept is decomposing shapes to simplify area calculations.

What happens to the area of figure B when a small square is moved to the outside?

• The area doubles

• The area remains the same

• The area decreases

• The area increases

How can you find the area of a shaded region on a grid without counting every square?

• By measuring the perimeter

• By using a calculator

• By estimating the area

• By decomposing the figure into smaller parts

When decomposing a figure on a grid, what is the first step?

• Count all the squares

• Identify smaller shapes within the figure

• Measure the perimeter

• Estimate the total area

What is the area of a triangle with a base of 2 units and a height of 4 units?

• 4 units squared

• 8 units squared

• 16 units squared

• 2 units squared

What is the formula for the area of a triangle?

• Base divided by height

• One-half base times height

• Base times height

• Base plus height

How do you find the area of a complex shape using subtraction?

• By dividing the shape into equal parts

• By adding all the parts together

• By subtracting the unshaded parts from a larger shape

• By multiplying the dimensions

How do you calculate the area of a shape that doesn't align with grid lines?

• By creating a larger shape and subtracting unshaded parts

• By counting the grid squares

• By using a ruler

• By estimating the area

What is the area of a 5 by 5 square with a 2 by 2 square removed from it?

• 23 units squared

• 25 units squared

• 21 units squared

• 20 units squared

What is the area of a triangle with a base of 3 units and a height of 5 units?

• 15 units squared

• 7.5 units squared

• 12.5 units squared

• 10 units squared

What is the keyword for this lesson?

• Subtract

• Decompose

• Triangle

• Area