Four triangles and one square form this pyramid with a square base. This means, we must find the surface area of all four triangles and the square.
Area of a triangle formula:
A=1/2•B•H
We need to modify this formula, however. Because the pyramid has four congruent triangle faces, we must multiply the area of one triangle by 4.
A=4(1/2•B•H)
Now, let’s input the triangle values into the modified formula. We know the base of the triangle is 4 inches because it lies on one of the square’s sides. Squares have congruent sides, so we know the base of the triangle.
A=4(1/2•4•6)
Simplify:
A=4(4•6)/2
A=4(24)/2
A=4(12)
A=48
So, all four triangles have a total area of 48in^2
Now, we must calculate the area of the square base.
Area of a square formula:
A=S^2, where S=side
Input the values of the square into the formula:
A=(4)^2
A=16
So, the square has an area of 16in^2.
Now, to find the surface area, we must add both areas from all four triangles and the square base:
Total area: 48+16=64
So, the surface area is 64in^2