Figure ABCDE has vertices A(-2, 3), B(2, 3), C(5,-2), D(0, -4), 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? (1 point) Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE. (4 points) Part C: What is the area of Figure ABCDE? Show your work. (5 points)​

9514 1404 393

  A: 1 rectangle and 2 triangles (or 1 trapezoid and 1 triangle)

  B: AB = 4; AE = 5

  C: area = 34.5 square units

Step-by-step explanation:

The figure can be decomposed into a right trapezoid and a triangle. The right trapezoid can be decomposed into a rectangle and a triangle.

easiest decomposition: 1 right trapezoid and 1 triangle

decomposition per instructions: 1 rectangle and 2 triangles.

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AB is a horizontal line, so its length is the difference of the x-coordinates of B and A: 2 -(-2) = 4.

AE is a vertical line, so its length is the difference of the y-coordinates of A and E: 3 -(-2) = 5.

  AB = 4, AE = 5

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The area of the trapezoid is given by ...

  A = 1/2(b1 +b2)h

The figure shows the base lengths to be 4 and 7, and the height to be 5. The trapezoid's area is ...

  A = 1/2(4+7)(5) = 27.5 . . . . square units

The area of triangle CDE is given by the formula ...

  A = 1/2bh

The figure shows the base length to be 7 and the height to be 2 units. The triangle area is ...

  A = 1/2(7)(2) = 7 . . . . square units

The total area of figure ABCDE is 27.5 +7 = 34.5 square units.

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