Final answer:
To calculate the height of a triangle from its area, the base must be known. Once given, the formula to find the height is rearranged to Height = (2 × Area) / base. Without the base, the height cannot be determined from the area alone.
Step-by-step explanation:
To find the height h of a triangle given its area, we use the formula for the area of a triangle: Area = 1/2 × base × height. If the area is 42 cm² but we are not given the base, we cannot directly calculate the height. However, if we know the base, we can rearrange the formula to solve for h: Height (h) = (2 × Area) / base.
For example, if we were given that the base of the triangle was 14 cm, we would calculate the height as follows:
- Height (h) = (2 × 42 cm²) / 14 cm
- Height (h) = 84 cm² / 14 cm
- Height (h) = 6 cm
Therefore, the height of the triangle would be 6 cm.