Answer:
Step-by-step explanation:
Rainy , 1st , let me mention that this type of problem isn't used for real world anything. The reason I mention that is b/c most times how much accuracy is needed is determined by the real world use of the math. That said, geometry problems are good for honing your math skills, which will be used for real world problems. so when you ask someone else to do the "honing" for you, you are missing out. :/ so i'll give you how to get the answer but not the answer
we are supposed to find the area. There are 3 shapes in the problem. 2 triangles and one rectangle.
we need to find the height of the triangles which is also the side of the rectangle.
to find the height of the triangles take the left one and use SOH CAH TOA to remember how trig functions fit. Nest use the appropriate trig function to solve the height. I'll set it up for you , you do that math
sin(45) = height / 8*[tex]\sqrt{2}[/tex]
8*[tex]\sqrt{2}[/tex]*sin(45) = height
next use the trig functions to find the base
cos(45) = base / 8*[tex]\sqrt{2}[/tex]
8*[tex]\sqrt{2}[/tex]*cos(45) = base
( I can do both of these in my head and you can too if you remember your trig functions? [also b/c it's a 45° triangle the base and the height are the same)
once you have the height use that with the area of a triangle funct.
1/2*base*height = area1
that gets you the area of the triangle on the left. next figure out the rectangle
height * 12 = area2 ( where height is the number you found above)
then solve for the last triangle on the right, the height is the same as the triangle on the left so you just need to find the base
Tan(30) = height / base
since you already know the height put that number in
base = height / Tan(30)
now you have the height and base of the triangle on the left
1/2*base*height = area3
add the 3 areas up and you have solved it :)