If the area of a triangle is 30 cm² and its base is 10 cm, what is the height of the triangle in cm?

• A. 5
• B. 6
• C. 7
• D. 8

Answer: (B)

To find the height of a triangle when the area and the base are known, you can use the formula for the area of a triangle:

[

\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

]

In this scenario, you have the area as 30 cm² and the base as 10 cm. Plugging the known values into the formula gives:

[

30 = \frac{1}{2} \times 10 \times \text{height}

]

Simplifying this, you can multiply both sides of the equation by 2 to eliminate the fraction:

[

60 = 10 \times \text{height}

]

Next, to solve for the height, divide both sides by 10:

[

\text{height} = \frac{60}{10} = 6 \text{ cm}

]

Thus, the height of the triangle is 6 cm. This aligns with the provided answer and shows that using the formula consistently leads to an accurate calculation of the height based on the area and base length.