Break down the figure into a cuboid and a triangle.
You have a cuboid with:
Height: 7cm
Length: 8cm
Width: 6cm
H x L = (7cmx8cm) = 56 cm^2
since there are 2 sides equal to each other (front and back) we add another 56 cm^2
Now calculate a side:
L x W = (8cmx6cm) = 48 cm^2
again, there are 2 sides equal to each other (top and bottom) we add another 48 cm^2
Finally, we calculate:
H x W = (7cmx6cm) = 42 cm^2
again, there are 2 sides equal to each other (right and left) we add another 42 cm^2
We add all up:
56 cm^2
56 cm^2
48 cm^2
48 cm^2
42 cm^2
42 cm^2
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SA: 292 cm^2 (This is the surface area of the cuboid)
Now we have to calculate the surface area of the triangle prism, but first we have to break it down into 2 triangles to make it easier; since they're equal in measure, their sides are equal too:
T1:
A (Height) = 7 cm
B (Base) = 6 cm
C (Hypotenuse) = 9 cm
Formula: A = 1/2 bh
A = 1/2 (6cm)(7cm)
A = 1/2 (42cm^2)
A = 21 cm^2
Therefore, you have 2 triangles with SA: 21 cm^2 each
We're not done yet.
Now calculate the bottom of the figure in the middle of the triangles. This is a rectangle and we can use the rectangle surface area formula to calculate it. We can do this by multiplying one side by the other:
Base = 6cm
Height = 6cm
B x H = (6cmx6cm) = 36 cm^2
There's another rectangle in the back of the triangles which is collided with the cuboid, this has the following mesuarements:
Base = 6cm
Height = 7cm
B x H = (6cmx7cm) = 42 cm^2
We have one last rectangle which is the one in the front in a slope. We simply do the same:
Base = 6cm
Height = 9cm
B x H = (6cmx9cm) = 56 cm^2
To calculate the surface area of the prism, add all up:
21 cm^2
21 cm^2
36 cm^2
42 cm^2
56 cm^2
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SA: 176 cm^2 (This is the surface area of the triangle prism)
The answer to your question "Find the surface area of the composite figure" is to simply add both surface areas up:
Cuboid SA: 292 cm^2
Triangle prism SA: 176 cm^2
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Composite figure SA: 468 cm^2
Hope this helps, I spent half an hour on this haha.
