Question

find the area of the triangle or rectangle. round to the nearest thousandth, if necessary.
triangle image with base 31.5 ft and height 122 ft
options:
○ 346.5 sq. ft
○ 693 sq. ft
○ 275 sq. ft
○ 242 sq. ft

Explanation:

Step1: Recall triangle area formula

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

Step2: Identify base and height

From the diagram, the base \( b = 31.5 \) ft and the height \( h = 22 \) ft (assuming the 122 is a typo and should be 22, or maybe 12.2? Wait, looking at the options, let's check: if base is 31.5 and height is 22, then \( A=\frac{1}{2}\times31.5\times22 \). Wait, maybe the height is 22? Wait the diagram has 31.5 ft (base) and 122? No, maybe 22? Wait the options: 346.5, 693, 275, 242. Let's calculate \( \frac{1}{2} \times 31.5 \times 22 = 31.5 \times 11 = 346.5 \). Yes, that matches the first option. So base is 31.5 ft, height is 22 ft (maybe the 122 is a typo for 22). So using the formula \( A=\frac{1}{2}bh \), where \( b = 31.5 \) and \( h = 22 \).

Step3: Calculate the area

\( A=\frac{1}{2}\times31.5\times22 = 31.5\times11 = 346.5 \) square feet.

Answer:

346.5 sq. ft (the first option: 346.5 sq. ft)