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.

step-by-step explanation:

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol