Answer:
28 cm²
Step-by-step explanation:
We are asked to find the surface area of the given square pyramid. To do this we can find the sum of the areas of each of the faces of the square pyramid, including the base.
Since this is a square pyramid, we know that each of the triangle faces of the pyramid have the same area, being the congruent triangles, and that there are 4 triangle faces.
Since this is a square pyramid, we know that the base of the pyramid is a square.
So to find the surface area we can multiply the area of one of the triangle faces by 4 and add it to the area of the square base. In other words:
(4 × area of triangle face) + area of square base = surface area
Lets start with finding the area of the square base. we are given that the side length of the base is 2 cm. Remember, the area of a square is:
s × s
or
s²
where s is the side length of the square.
Lets plug in 2 for s:
2 × 2 = 4
or
2² = 4
So the area of the square base is 4 cm².
Now lets find the area of the triangle side.
Remember, the area of a triangle is:
where b is the length of the base (not to be confused with the base of the pyramid) and h is the height.
We are given that the height of the pyramid is 6 cm and the base is 2 cm. Lets plug in 6 for h and 2 for b:
So the area of a triangle side of the pyramid is 6 cm².
Now lets find the surface area. To do this we can multiply the area of a triangle side of the pyramid by 4 and add the area of the square base. Remember, the area of the square base was 4 cm² and the area of the triangle side was 6 cm².
(4 × 6) + 4 = 24 + 4 = 28
So the surface area would be 28 cm²
I hope this helps. Let me know if you have any questions. Happy studying.
