Question

I rlly need help on this geometry study guide question

Answer 1

145.2 feet squared

Explanation:

The area of a triangle is calculated using the formula:

`Area=(1)/(2)* Base* Height`

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.

`\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=√(28.6^2-11^2) \\ Altitude=26.4\;ft \end{gathered}`

The height of the triangle is 26.4 ft.

Using this, we can then find the area.

`\begin{gathered} Area=(1)/(2)*11*26.4 \\ =145.2\;ft^2 \end{gathered}`

The area of the triangle is 145.2 feet squared.