I'll solve the problem of finding the area of each equilateral triangle using the provided formula.
First, let me understand what I'm looking at:
- The image shows 6 different equilateral triangles labeled 1 through 6.
- Each triangle has a side length given (in cm).
- At the bottom, there's a formula for the area of an equilateral triangle: A = (√3/4) × s², where s is the length of one side.
Let me calculate the area for each triangle:
Triangle 1:
- Side length (s) = 8 cm
- Area = (√3/4) × 8² = (√3/4) × 64 = 16√3 ≈ 27.71 cm²
Triangle 2:
- Side length (s) = 12 cm
- Area = (√3/4) × 12² = (√3/4) × 144 = 36√3 ≈ 62.35 cm²
Triangle 3:
- Side length (s) = 5 cm
- Area = (√3/4) × 5² = (√3/4) × 25 = (25√3)/4 ≈ 10.83 cm²
Triangle 4:
- Side length (s) = 2.5 cm
- Area = (√3/4) × 2.5² = (√3/4) × 6.25 = (6.25√3)/4 ≈ 2.70 cm²
Triangle 5:
- Side length (s) = 6.2 cm
- Area = (√3/4) × 6.2² = (√3/4) × 38.44 = (38.44√3)/4 ≈ 16.65 cm²
Triangle 6:
- Side length (s) = 8.5 cm
- Area = (√3/4) × 8.5² = (√3/4) × 72.25 = (72.25√3)/4 ≈ 31.27 cm²
The solution involves applying the formula A = (√3/4) × s² to each triangle, where s is the given side length for that triangle. This formula is derived from the properties of equilateral triangles and the Pythagorean theorem, as the height of an equilateral triangle can be calculated as (√3/2) × s, and then using the standard triangle area formula (1/2) × base × height.
Parent Tip: Review the logic above to help your child master the concept of area of a right triangle worksheet.
