Find the area of the composite figure

The area of the composite figure = 32 + 6 + 6 = 44 units²

Step-by-step explanation:

* To find the area of this composite figure lets divide it into 3

  familiar figures trapezium and 2 triangles

* The vertices of the trapezium are:

  (3 , 2) , (3 , -1) , (-5 , -3) , (-5 , 2)

∵ The vertices of the parallel bases are:

   Small base ⇒ (3 , 2) and (3 , -1) its length = 2 - -1 = 3 units ⇒

   vertical distance (same x-coordinates)

   Large base ⇒ (-5 , -3) and (-5 , 2) its length = 2 - -3 = 5 units ⇒

   vertical distance (same x-coordinates)

   The vertices of the its height are:

   (3 , 2) and (-5 , 2) its length = 3 - -5 = 8 ⇒ horizontal distance

   (same y-coordinates)

∵ Area trapezium = 1/2 (base1 + base2) × height

∴ Its area = 1/2 × (3 + 5) × 8 = 32 units² ⇒ (1)

* The vertices of the 2 triangles are:

  First Δ: (3 , 2) , (-1 , 2) , (1 , 5)

  The length of its base = 3 - -1 = 4 ⇒ horizontal distance

   (same y-coordinates)

   The length of its height = 3 (at x = 1 the ⊥ distance from the

   vertex to the base = 5 - 2 = 3)

∵ The area of the Δ = 1/2 (base)(height)

∴ Its area = 1/2 × 4 × 3 = 6 units² ⇒ (2)

  Second Δ: (-1 , 2) , (-5 , 2) , (-3 , 5)

  The length of its base = -1 - -5 = 4 ⇒ horizontal distance

  (same y-coordinates)

   The length of its height = 3 (at x = -3 the ⊥ distance from the

   vertex to the base = 5 - 2 = 3)

∵ The area of the Δ = 1/2 (base)(height)

∴ Its area = 1/2 × 4 × 3 = 6 units² ⇒ (3)

Add (1) , (2) and (3)

∴ The area = 32 + 6 + 6 = 44 units²

do you mean add both of the equations together

because if you do the answer is 10x-5

step-by-step explanation:

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europa2433

step-by-step explanation: