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.
