Understanding Areas Under Graphs

The video tutorial explains how to calculate the area under a graph bounded by the horizontal axis and vertical lines at specific points. It covers the calculation of areas A of 1, 2, 3, and 4 using geometric shapes like trapezoids and rectangles. Each section provides a step-by-step guide to applying the appropriate area formulas, ensuring a clear understanding of the process.

What does A(x) represent in the context of the graph?

• The slope of the graph

• The area bounded by the graph, horizontal axis, and vertical lines

• The volume under the graph

• The length of the graph

Which formula is used to calculate the area of a trapezoid?

• Base x Height

• 1/2 x (Base1 + Base2) x Height

• 1/3 x Base x Height

• Length x Width

What is the area of A(1) in square units?

• 5

• 8

• 6

• 7

How is the area of A(2) calculated?

• By multiplying the area of A(1) by 2

• By subtracting the area of a rectangle from A(1)

• By adding the area of a rectangle to A(1)

• By adding the area of a triangle to A(1)

What is the total area of A(2) in square units?

• 11

• 10

• 12

• 13

What shape is A(3) and how is its area calculated?

• Rectangle, using Length x Width

• Circle, using π x Radius^2

• Triangle, using 1/2 x Base x Height

• Trapezoid, using 1/2 x (Base1 + Base2) x Height

What is the total area of A(3) in square units?

• 15.5

• 14.5

• 16.5

• 13.5

What is the shape of A(4) and how is its area calculated?

• Rectangle, using Length x Width

• Triangle, using 1/2 x Base x Height

• Trapezoid, using 1/2 x (Base1 + Base2) x Height

• Circle, using π x Radius^2

What is the total area of A(4) in square units?

• 18.5

• 17.5

• 16.5

• 19.5

Which of the following is NOT a method used to calculate areas in this tutorial?

• 1/3 x Base x Height

• π x Radius^2

• Length x Width

• 1/2 x (Base1 + Base2) x Height