Answer:
(9 + 6x) ft²
Step-by-step explanation:
The surface area of a 3D figure is just the area of all of its sides added together. You can also think of it as the area of the shapes that you would see if you "opened" it up and laid it flat.
This square pyramid is made up of one square, on the bottom, and four triangles. So what you need to do is find the area of the square, and then add it to the area of the four triangles.
Let's start with the square.
We know that the area of a square is A = s² = s × s.
Since we know that s is 3 feet, we can just substitute 3 into the formula to find the area of the square.
A = s² ⇒ (3)² = 3 × 3 = 9
The area of the square is 9 ft².
Now, we need to find the areas of the four triangles.
We know that the area of a triangle is A = [tex]\frac{1}{2}[/tex] bh.
Since we know that b is 3 and h is x, we can just substitute 3 and x into this formula to find the area of a triangle.
A = [tex]\frac{1}{2}[/tex] (3) (x) = 1.5x
But we're not done yet; we have four triangles, not just one. 1.5x is the area of one triangle, so to find the area of four, all we have to do is multiply 1.5x by 4. This gives us 6x ft².
Now we're on our last step. We can add 9 ft² to 6x ft² to get (9 + 6x) ft², and you're done.
