Answer:
84in²
Explanation:
What is surface area?
Surface area is the area that covers the outside of a three dimensional object.
Here, we are trying to find the surface area of a square pyramid which consists of 4 triangles and a square. The surface area would be the sum of the areas of those shapes as that is what covers the outside of the square pyramid.
Finding the surface area.
Finding the area of the square :
Area of a square = s² where s = side length of square.
Here, it appears that the side length of the square has a measure of 6 in
So area = 6² = 6 × 6 = 36in²
Finding the area of the 4 triangles
Area of a triangle = bh/2 where b = base length and h = height
Here, the triangle shares its base length with the side length of the square so the base length or "b" = 6. The height or "h" is 4.
So we have A = bh/2
==> plug in b = 6 and h = 4
A = (6)(4)/2
==> multiply 6 and 4
A = 24/2
==> divide 24 by 2
A = 12
There are 4 triangles so we multiply the area of 1 triangle by 4 to get the area of all the triangles
Area of all triangles = 12 × 4 = 48
Finally we add the two areas together to get the total surface area
Area of square = 36
Area of triangles = 48
Total surface area = 36 + 48 = 84in²