Step 1: Recall the triangle area formula: Area = (1/2) × base × height

Step 2: Identify the given values: Base = 12 cm Height = 8 cm

Step 3: Substitute into the formula: Area = (1/2) × 12 × 8 Area = (1/2) × 96 Area = 48 cm²

Answer: The area is 48 cm²

Use the formula: $A = \frac{1}{2}bh$

$A = \frac{1}{2}(10)(6)$

$A = \frac{60}{2} = 30$

Answer: 30 square units

Step 1: Recall the parallelogram area formula: Area = base × height

Step 2: Identify the values: Base = 15 m Height = 9 m (perpendicular distance)

Step 3: Calculate: Area = 15 × 9 Area = 135 m²

Step 4: Note: The height must be perpendicular to the base It's NOT the length of the slanted side

Answer: The area is 135 m²

Use the trapezoid formula: $A = \frac{1}{2}(b_1 + b_2)h$

$A = \frac{1}{2}(8 + 12)(5)$

$A = \frac{1}{2}(20)(5)$

$A = 50$

Answer: 50 square units

Step 1: Recall the trapezoid area formula: Area = (1/2) × (base₁ + base₂) × height

Step 2: Identify the values: Base₁ = 10 cm Base₂ = 16 cm Height = 7 cm

Step 3: Substitute: Area = (1/2) × (10 + 16) × 7 Area = (1/2) × 26 × 7 Area = (1/2) × 182 Area = 91 cm²

Step 4: Alternative thinking: Average of bases = (10 + 16)/2 = 13 cm Area = average × height = 13 × 7 = 91 cm²

Answer: The area is 91 cm²

Step 1: Recall the rhombus area formula: Area = (1/2) × d₁ × d₂ where d₁ and d₂ are the diagonals

Step 2: Identify the diagonals: d₁ = 14 cm d₂ = 10 cm

Step 3: Calculate: Area = (1/2) × 14 × 10 Area = (1/2) × 140 Area = 70 cm²

Step 4: Why this formula works: The diagonals of a rhombus are perpendicular They divide the rhombus into 4 right triangles Total area = sum of the 4 triangles

Answer: The area is 70 cm²

For a rhombus, use the diagonal formula: $A = \frac{1}{2}d_1 d_2$

$A = \frac{1}{2}(10)(24)$

$A = \frac{240}{2}$

$A = 120$

Answer: 120 square units

Step 1: Recall Heron's formula: Area = √[s(s-a)(s-b)(s-c)] where s is the semi-perimeter: s = (a+b+c)/2

Step 2: Find the semi-perimeter: a = 13, b = 14, c = 15 s = (13 + 14 + 15)/2 s = 42/2 s = 21

Step 3: Calculate (s - a), (s - b), (s - c): s - a = 21 - 13 = 8 s - b = 21 - 14 = 7 s - c = 21 - 15 = 6

Step 4: Substitute into Heron's formula: Area = √[21 × 8 × 7 × 6] Area = √[21 × 8 × 7 × 6] Area = √7056

Step 5: Simplify the square root: 7056 = 16 × 441 = 16 × 21² √7056 = 4 × 21 = 84

Step 6: Verify the calculation: 21 × 8 = 168 168 × 7 = 1176 1176 × 6 = 7056 √7056 = 84 ✓

Answer: The area is 84 square units