Question

what is the area of a right triangle with a height of 8.9 cm and a base of 14.3 cm?

Explanation:

Step1: Recall the formula for the area of a triangle

The area \( A \) of a triangle is given by the formula \( A=\frac{1}{2}\times\text{base}\times\text{height} \). For a right triangle, the base and height are the two legs of the right angle.

Step2: Substitute the given values into the formula

Here, the base \( b = 14.3\space\text{cm} \) and the height \( h=8.9\space\text{cm} \). Substituting these into the formula, we get \( A=\frac{1}{2}\times14.3\times8.9 \).

Step3: Perform the multiplication

First, calculate \( 14.3\times8.9 \). \( 14.3\times8.9 = 14.3\times(9 - 0.1)=14.3\times9-14.3\times0.1 = 128.7- 1.43=127.27 \). Then, multiply by \( \frac{1}{2} \): \( A=\frac{127.27}{2}=63.635 \space\text{cm}^2 \).

Answer:

The area of the right triangle is \( 63.635\space\text{cm}^2 \) (or approximately \( 63.64\space\text{cm}^2 \) if rounded to two decimal places).