Question

if the area of a triangle is 45 cm² and its base is 9 cm, what is its height?

Explanation:

Step1: Recall the area formula of a triangle

The area formula of a triangle is \( A=\frac{1}{2}\times b\times h \), where \( A \) is the area, \( b \) is the base, and \( h \) is the height.

Step2: Rearrange the formula to solve for height

From \( A = \frac{1}{2}\times b\times h \), we can get \( h=\frac{2A}{b} \).

Step3: Substitute the given values into the formula

Given \( A = 45\ \text{cm}^2 \) and \( b=9\ \text{cm} \), then \( h=\frac{2\times45}{9} \).
Calculate \( 2\times45 = 90 \), so \( h=\frac{90}{9}=10\ \text{cm} \).

Answer:

\( 10\ \text{cm} \)