Find the exact area of each triangle using the formula 𝓐 = ½ bh, and then verify that Heron's formula gives the same result.


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Verified step by step guidance

1. Identify the base (b) and height (h) of the triangle from the given image. The base is typically one side of the triangle, and the height is the perpendicular distance from this base to the opposite vertex.
2. Apply the area formula for a triangle, \( A = \frac{1}{2} bh \), by substituting the values of base and height that you identified.
3. To use Heron's formula, first calculate the semi-perimeter of the triangle, which is half the sum of all three sides, \( s = \frac{a+b+c}{2} \), where a, b, and c are the lengths of the sides of the triangle.
4. Apply Heron's formula: \( A = \sqrt{s(s-a)(s-b)(s-c)} \), where s is the semi-perimeter calculated in the previous step, and a, b, and c are the side lengths of the triangle.
5. Compare the area obtained from the basic area formula \( \frac{1}{2} bh \) with the area obtained from Heron's formula to verify if they give the same result.