Question

Three sides of a triangle are 1, 1 and 0.5 meters in length. The area of the triangle in m² is ............. (decimal digits up to 2 places)

Hint:

Use Heron's formula to calculate the area of a triangle when you know the lengths of all three sides.

Answer 1

Correct Answer: 0.23

Step 1: Use Heron's formula to calculate the area.
Heron's formula for the area of a triangle is given by: \[ A = \sqrt{s(s-a)(s-b)(s-c)}, \] where \( s \) is the semi-perimeter of the triangle and \( a, b, c \) are the sides of the triangle. First, calculate the semi-perimeter \( s \): \[ s = \frac{a + b + c}{2} = \frac{1 + 1 + 0.5}{2} = 1.25 \, \text{meters}. \]

Step 2: Apply Heron's formula.
Now apply Heron's formula: \[ A = \sqrt{1.25(1.25 - 1)(1.25 - 1)(1.25 - 0.5)} = \sqrt{1.25 \times 0.25 \times 0.25 \times 0.75} = 0.24 \, \text{m}^2. \]

Step 3: Conclusion.
The area of the triangle is 0.24 m².