Area P.5

Form 1-5 Mathematics

Area of polygon (P.5)

This is a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright & copy ; 1990-1998 by Key Curriculum Press, Inc. All rights reserved. Portions of this work were funded by the National Science Foundation (awards DMI 9561674 & 9623018).

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Sorry that I didn't post P.1 - P.4 in the Internet as I used some Java applets from IES.

Problem 5

E is a point on the line BC. The angle < AEB and the lengths of AE and BC are given. Can you find the area of the triangle ABC? (Note that E may bot be on the line segment BC.)
Does the position of E affect the area of the traingle ABC? Drag E to observe.
Click the button "Answer" to check your answer. Can you prove your answer?
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Problem 6
We would like to find a formula for the area of any quadrilateral ABCD if the lengths of the diagonals AC and BD are known and the angle < AEB is known.

Drag the free points to investigate the relationship among the areas of different polygons. Can you find a formula for the area of ABCD? Draw a diagram using Cabri or Sketchpad and test your results.
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