Hey there!
To find the surface area of this solid, we will want to find the surface area of the two 3d shapes we are given and then add them.
SQUARE PRISM
For the square prism, we want to find the area of the front, back, two sides, top, and bottom.
FRONT AND BACK
As we can see, one side length for the front and back is 5. The one that goes upward is 4. If we multiply the two, we get twenty. Therefore, the front and back are each twenty square feet.
20+20= 40
SIDES
Now, we want to find the two sides. These have the same dimensions as the front and back: a 5 and a four. This is two twenties once again.
20+20=40
TOP AND BOTTOM
Now, we want to find the top and bottom. Our two lengths on the bottom are 5 and 5, so this area will be 25 on the bottom and 25 on the top. However, in our final solid, you cannot see the top part of the cube because it is covered up by the square pyramid, therefore, we will just use one of our 25s.
25
Now, let's add up these areas to see the surface area of the square prism.
25+40+40= 105 square feet.
SQUARE PYRAMID
To find the surface area of our square pyramid, we want to find the area of the four triangles and then add them up. We will not count the actual base because it's not part of the surface of the solid, so it is not part of the surface area.
TRIANGLE FACES
The formula for a triangle is 1/2 multiplied by the base times the height. We have four congruent triangles so we can multiply this result by four.
Our base is 5, our height is six, we multiply both by 1/2 and four, and we will then get our answer.
4*1/2*5*6= 60
Therefore, the surface area of our square pyramid is 60 square inches.
COMPOSITE SOLID
Now, we simply add up the two surface areas we gathered.
Square Prism: 105 square feet
Square Pyramid: 60 feet
105+60=165
Therefore, the surface area is 165 square feet.
I hope that this helps! Have a wonderful day!
