Figure ABCDE has vertices A(−2, 3), B(2, 3), C(5, −2), D(0, −3), and E(−2, −2). Plot the points on your own coordinate grid and
connect the points in alphabetical order. Decompose Figure ABCDE into rectangles and triangles.
Part A: How many triangles and rectangles did you make?
Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE.
Part C: What is the area of Figure ABCDE? Show your work.
Part A: How many triangles and rectangles did you make?
Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE.
Part C: What is the area of Figure ABCDE? Show your work.
1 answer:
A) The figure decomposes nicely into 1 rectangle and 2 triangles.
B) AB = 4 units; AE = 5 units.
C) The rectangle whose diagonal is BE has area 4*5 = 20 units^2.
.. The triangle CDE has area (1/2)*7*1 = 7/2 units^2.
.. The triangle BCF has area (1/2)*3*5 = 15/2 units^2.
The total area of the figure is
.. area = rectangle + triangle CDE + triangle BCF
.. = (20 +7/2 +15/2) units^2
.. = 31 units^2
_____
Check:
.. Compare our computed value of area to that listed for poly1 on the left side of the figure.
B) AB = 4 units; AE = 5 units.
C) The rectangle whose diagonal is BE has area 4*5 = 20 units^2.
.. The triangle CDE has area (1/2)*7*1 = 7/2 units^2.
.. The triangle BCF has area (1/2)*3*5 = 15/2 units^2.
The total area of the figure is
.. area = rectangle + triangle CDE + triangle BCF
.. = (20 +7/2 +15/2) units^2
.. = 31 units^2
_____
Check:
.. Compare our computed value of area to that listed for poly1 on the left side of the figure.
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