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zysi [14]
2 years ago
6

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

Mathematics
2 answers:
Rama09 [41]2 years ago
4 0

Solution:

<u>Finding the area of triangle₁</u>

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

<u>Finding the area of triangle₂</u>

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

<u>Finding the area of triangle₃</u>

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

<u>Finding the area of rectangle</u>

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

<u>Finding the area of quadrilateral</u>

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

<u>Verifying Option A</u>

  • (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
  • => <u>42 units²</u>

Option A is correct.

<u>Verifying Option B</u>

  • (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

<u>Verifying Option C</u>

  • (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

<u>Verifying Option D</u>

  • 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
  • => <u>42 units²</u>

Option A and D are correct.

marissa [1.9K]2 years ago
3 0

Answer:

A) and D)

Step-by-step explanation:

The area of the quadrilateral = 42 square units

A) 42

B) 50

C) 54

D) 42

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