Understanding Area Under a Graph

This lesson covers how to determine the area under a graph using geometric formulas. It includes examples such as calculating the distance traveled by a car, the manufacturing cost of phones, and the cost of growing mesquite trees. The lesson explains the significance of the area under a graph and introduces the concept of using rectangles for approximation in cases where geometric formulas are not applicable.

What is the primary goal of using area formulas in this lesson?

• To calculate the perimeter of a graph

• To find the area under a graph using geometric formulas

• To determine the volume under a graph

• To measure the height of a graph

In the car example, what does the area under the graph represent?

• The time taken for the journey

• The fuel efficiency of the car

• The total distance traveled

• The speed of the car

How is the area under the manufacturing cost graph calculated?

• By estimating with a triangle

• By using a single rectangle

• By dividing the area into four rectangles and summing them

• By using a circle

What does the area under the manufacturing cost graph represent?

• The profit from selling the phones

• The average cost per phone

• The total cost of manufacturing the phones

• The total number of phones produced

Tags

CCSS.HSA.CED.A.1

How is the average cost per phone calculated in the manufacturing example?

• By adding the total cost to the number of phones

• By subtracting the total cost from the number of phones

• By multiplying the total cost by the number of phones

• By dividing the total cost by the number of phones

What type of function is used in the mesquite tree example?

• A logarithmic function

• A linear function

• A quadratic function

• An exponential function

Tags

CCSS.HSF.LE.B.5

What shape is used to find the area under the graph in the mesquite tree example?

• Rectangle

• Triangle

• Circle

• Trapezoid

Tags

CCSS.HSF.LE.B.5

What does the area under the graph represent in the mesquite tree example?

• The profit from selling the trees

• The average height of the trees

• The total cost of growing the trees

• The total number of trees grown

What is the next topic to be covered after this lesson?

• Using circles to find area under a curve

• Finding the perimeter of a curve

• Approximating area under a curve using rectangles

• Calculating volume under a curve

Why might geometric formulas not always be used to find the area under a curve?

• Because they are not accurate

• Because the curve might not form simple shapes

• Because they are too complex

• Because they require too much time