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

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.