Question

find the area of the following triangle:
triangle diagram with side lengths 11, 18, 14 and a dashed height of 9 (with right angle) to the side of length 18
note: figure may not be drawn to scale.
label optional
input box
buttons: trash, undo, etc.

Explanation:

Step1: Recall the formula for the area of a triangle

The area of a triangle is given by the formula \( A = \frac{1}{2} \times \text{base} \times \text{height} \).

Step2: Identify the base and height

From the diagram, the base of the triangle (the side to which the height is perpendicular) is 18, and the corresponding height is 9.

Step3: Substitute the values into the formula

Substitute base \( = 18 \) and height \( = 9 \) into the formula:
\[
A = \frac{1}{2} \times 18 \times 9
\]

Step4: Calculate the area

First, calculate \( \frac{1}{2} \times 18 = 9 \). Then, multiply this result by 9: \( 9 \times 9 = 81 \).

Answer:

81