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Select all expressions that represent the area of the quadrilateral shown.

Select All Expressions That Represent The Area Of The Quadrilateral Shown class=

Sagot :

Semsee45idn

Answer:

A) and D)

Step-by-step explanation:

The area of the quadrilateral = 42 square units

A) 42

B) 50

C) 54

D) 42

Solution:

Finding the area of triangle₁

  • 1/2 x 6 x 2 = Area of triangle₁
  • => 6 units² = Area of triangle₁

Finding the area of triangle₂

  • 1/2 x 8 x 2 = Area of triangle₂
  • => 8 units² = Area of triangle₂

Finding the area of triangle₃

  • 1/2 x 4 x 2 = Area of triangle₃
  • => 4 units² = Area of triangle₃

Finding the area of rectangle

  • 6 x 4 = Area of rectangle
  • => 24 units² = Area of rectangle

Finding the area of quadrilateral

  • 6 + 8 + 4 + 24 = Area of quadrilateral
  • => 42 units² = Area of quadrilateral

Verifying Option A

  • (8 x 8) - 1/2(8 x 2) - 1/2(2 x 4) - (2 x 2) - 1/2(6 x 2)
  • => (64) - 1/2(16) - 1/2(8) - (4) - 1/2(12)
  • => 64 - 8 - 4 - 4 - 6
  • => 42 units²

Option A is correct.

Verifying Option B

  • (8 x 4) - 1/2(2 x 4) + (2 x 8) + 1/2(2 x 6)
  • => 32 - 1/2(8) + (16) + 1/2(12)
  • => 32 - 4 + 16 + 6
  • => 50 units²

Verifying Option C

  • (8 x 8) - 1/2(8 x 2) - 1/2(2 x 4) - 1/2(6 x 2)
  • => (64) - 1/2(16) - 1/2(8) - 1/2(12)
  • => (64) - 8 - 4 - 6
  • => 46 units²

Verifying Option D

  • 1/2(8 x 2) + 1/2(4 x 2) + (4 x 6) + 1/2(6 x 2)
  • => 1/2(16) + 1/2(8) + (24) + 1/2(12)
  • => 8 + 4 + (24) + 6
  • => 42 units²

Option A and D are correct.

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