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I WILL IVE U 5 STARS
Figure ABCDE has vertices A(−3, 3), B(2, 3), C(5, −2), D(0, −3), and E(−3, −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.

Sagot :

sqdancefan

Answer:

  A. 1 rectangle, 2 triangles

  B. AB = AE = 5

  C. 36.5 square units

Step-by-step explanation:

A.

The attached figure shows 1 rectangle (square) and two triangles.

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B.

These sides are aligned with the grid, so their length is simply the difference in coordinates along the line:

  AB = 2 -(-3) = 5

  AE = 3 -(-2) = 5

__

C.

The area of the square is ...

  A = s^2 = 5^2 = 25

The area of triangle BCF is ...

  A = 1/2bh = 1/2(3)(5) = 15/2

The area of triangle CDE is ...

  A = 1/2bh = 1/2(8)(1) = 4

The total area is the sum of the areas of the square and two triangles:

  total area = 25 +7.5 +4 = 36.5 . . . square units

_____

Additional comment

We note that segment CE divides the figure into trapezoid ABCE and triangle CDE. The trapezoid has bases 5 and 8, and height 5, so its area is ...

  A = 1/2(b1 +b2)h = 1/2(5 +8)(5) = 32.5

Triangle CDE has the same area as computed above, 4 square units. So, the total area of the figure is ...

  32.5 +4 = 36. 5 . . . . square units

View image sqdancefan
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