Question

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

Answer 1

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.

Answer 2

A) and D)

Explanation:

The area of the quadrilateral = 42 square units

A) 42

B) 50

C) 54

D) 42