The surface area of any object is the sum of the areas of all the faces. In this case, we have a rectangular prism with dimensions 8x4x3 and a trianglar prism with a 8x4 rectangular base and height of 6.
Let's start with the rectangular prism. We have the bottom which is 8x4, two sides that are 3x4, and two sides that are 8x3.
8*4 + 2*3*4 + 2*8*3 = 104 in^2
Now that's find the surface area of the trianglar prism. We have the rectangular side on top which is 10x4, the rectangular side on the right which is 6x4, and two triangles that are 8 long and 6 high.
10*4 + 6*4 + 2*0.5*8*6 = 112 in^2
The total surface area is 104 + 112 = 216 in^2
Acronym to remember the 3 basic trigonomic functions:
Soh - Cah - Toa
opposite
sin = --------------------
hypotenuse
adjacent
cos = -------------------
hypotenuse
opposite
tan = -----------------
adjacent
In your case, you can set up a sine trigonomic function, like this:
Sin 48 = 10 (adjacent)
-----
x (hypotenuse)
10
(x) Sin 48 = ------ (x)
x
(x) Sin 48 = 10
-------------- -------------
Sin 48 Sin 48
Plug in 10(sin)(48) into a calculator.
x = 7.43
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Answer:
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