Mathematics
Grade9
Easy

Question

In the given triangular pyramid, ABCP, YZ is the midsegment of increment APC, XZ is the midsegment of increment ABC, XY is the midsegment of increment ABP. Which of the following statement is true?

  1. Area of increment BPC = 1 fourth Area of increment XYZ
  2. Area of ∆ XYZ = 2 Area of ∆ BPC
  3. Area of ∆ABC = Area of ∆ABP
  4. All the above

Hint:

Area of triangle is 1 half cross times b a s e cross times h e i g h t

The correct answer is: Area of increment BPC = 1 fourth Area of increment XYZ


    Area of ∆BPC = 1 half space cross times space 1 half height of ∆XYZ  cross times space 1 half base of ∆XYZ
    = 1 fourth Area of ∆XYZ

    The midpoint theorem refers to the midpoint of the line segment. It defines the coordinate points of the midpoint of the line segment and can be found by taking the average of the coordinates of the given endpoints. 

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