Question

find the area of the triangle.
b = 108 in.
h = 4 ft

the area of the triangle is \\(\square\\) \\(\text{in}^2\\) or \\(\square\\) \\(\text{ft}^2\\).
(type whole numbers.)

Explanation:

Step1: Convert height to inches

Since 1 ft = 12 in, \( h = 4\times12 = 48 \) in.

Step2: Calculate area in square inches

The formula for the area of a triangle is \( A=\frac{1}{2}bh \). Substituting \( b = 108 \) in and \( h = 48 \) in, we get \( A=\frac{1}{2}\times108\times48 \).
First, \( 108\times48 = 5184 \), then \( \frac{1}{2}\times5184 = 2592 \) \( \text{in}^2 \).

Step3: Convert base to feet

Since 1 ft = 12 in, \( b=\frac{108}{12}=9 \) ft.

Step4: Calculate area in square feet

Using the area formula \( A=\frac{1}{2}bh \) with \( b = 9 \) ft and \( h = 4 \) ft, we get \( A=\frac{1}{2}\times9\times4 \).
First, \( 9\times4 = 36 \), then \( \frac{1}{2}\times36 = 18 \) \( \text{ft}^2 \).

Answer:

The area of the triangle is \( 2592 \) \( \text{in}^2 \) or \( 18 \) \( \text{ft}^2 \).