Question

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: After you plot the points on your coordinate grid. Describe in detail the process used to solve for the area

Part B: What is the area?

Answer 1

Answer:

Part A. See below.

Part B. 6

Step-by-step explanation:

Figure ABCDE consists of two triangles.

Part A. How to calculate the area.

Area = area of ∆ADE  + area of ∆BCD

The formula for the area of a triangle is  

A = ½bh

Note that the triangles are "upside-down." The bases are at the top.

For ∆ADE:

b = AD = x₂ - x₁ = 0 - (-2) = 2

h = AE = y₂ - y₁ = 3 -    2   = 1

For ∆BCD:

b = BD = x₂ - x₁ = 0 - (-2) = 2

h = BF = y₂ - y₁ = 3 - (-2) = 5

Part B. Calculating the area.

For ∆ADE:

A = ½ × 2 × 1 = 1

For ∆BCD:

A = ½ × 2 × 5 = 5

For ABCDE:

A = 1 + 5 = 6

The area of the figure is 6 square units.