Answer:
144mi^2
Step-by-step explanation:
The first step would be to find the top and bottom of the shape which are two triangles.
The way you find the area of a triangle is
[tex]A= \frac{L*W}{2}[/tex]
The length is 6 and the width is 8 so you can plug in the numbers
[tex]A=\frac{6*8}{2}[/tex]
Then multiply 6 by 8
[tex]A=\frac{48}{2}[/tex]
And divide by two
[tex]A=24[/tex]
because there are two identical triangles, multiply 24 by 2 to get 48.
The two triangles make 48mi
Now you must find the area of all the rectangles on the sides separately.
The way to find the area of a rectangle is
[tex]A=L*W[/tex]
You must do one at a time, first, I will so the side with a length of 4 and width of 10
[tex]A=4*10[/tex]
Multiply 4 by 10 to get
[tex]A=40[/tex]
One of the rectangles has the area of 40mi
Now you must find the area of the other rectangles with the same formula. I will be doing the one with a length of 4 and a width of 8 next
[tex]A=4*8[/tex]
Multiply 4 by 8 to get
[tex]A=32[/tex]
The area of the second rectangle is 32mi
Finally, you want to find the area of the last rectangle that has a length of 4 and a width of 6. We will be using the same formula again
[tex]A=4*6[/tex]
Multiply 4 by 6 to get
[tex]A=24[/tex]
The area of the last rectangle is 24mi
The last step is to add all the areas together to get the surface area of the figure.
First the two triangles, then the first rectangle, the second, and finally the third.
[tex]SA = 48+40+32+24[/tex] (SA is surface area)
Once you add them all, you get
[tex]SA=144[/tex]
So the Surface area of the whole figure is 144mi^2
Hope this helps!
Feel free to ask any other questions if you have any.
Have a good day! :)
