Answer:
145.2 feet squared
Explanation:
The area of a triangle is calculated using the formula:
[tex]Area=\frac{1}{2}\times Base\times Height[/tex]
In the given right triangle:
• The hypotenuse = 28.6 ft
,
• The base = 11 ft
First, we find the height of the triangle using the Pythagorean Theorem.
[tex]\begin{gathered} Hypotenuse^2=Base^2+Altitude^2 \\ 28.6^2=11^2+Altitude^2 \\ Altitude^2=28.6^2-11^2 \\ Alt\imaginaryI tude=\sqrt{28.6^2-11^2} \\ Altitude=26.4\;ft \end{gathered}[/tex]
The height of the triangle is 26.4 ft.
Using this, we can then find the area.
[tex]\begin{gathered} Area=\frac{1}{2}\times11\times26.4 \\ =145.2\;ft^2 \end{gathered}[/tex]
The area of the triangle is 145.2 feet squared.
