Greetings!
Answer:
230.65
Step-by-step explanation:
If two sides are the same (two sides measure 23.66) this means the triangle is an isoceles triangle. The equation for area of an isoceles triangle is as follows:
[tex]\frac{1}{2}[/tex] x base x height.
As you have the size of the base, you need to find the area of the height.
As this turns into a pythagoras' theory question, you need to reacall:
[tex]a^2 + b^2 = c^2[/tex]
To get the b^2 value we need to divide the total base (22.8) value in two:
22.8 ÷ 2 = 11.4
So, as you have the hypotenuse ([tex]c^2[/tex]) and the base ([tex]b^2[/tex]) we need to find the [tex]a^2[/tex] value.
To do this we need to subtract the [tex]b^2[/tex] value from the [tex]c^2[/tex] value:
[tex]c^2 - b^2 = a^2[/tex]
Plug the values in:
[tex]23.66^2 - 11.4^2 = a^2[/tex]
So [tex]a^2 = 429.8356[/tex]
Simply square root this to find a:
a = 20.7325
Now we have all the possible value, we need to plug them into the area formula which was:
[tex]\frac{1}{2}[/tex] x base x height
Plug the values in:
[tex]\frac{1}{2} * 22.8 * 20.2325[/tex]
= 230.6505
So the area is 230.65 feet!
Hope this helps!
