The pyramid given above has four faces. Each of which are in triangular shape. The area of the triangle is calculated through the equation,
A = bh / 2
where A is area, b is base and h is the height.
Substituting the known values,
A = (4 inch)(9 inch) / 2 = 18 in²
Multiplying this area by 4 will give us an answer of 72 in².
Then, we also calculate for the area of the square base.
A = s²
where s is the measure of each side of the square.
A = (4 in)² = 16 in²
Finally, we add up the calculated areas.
surface area = 72 in² + 16 in²
surface area = 88 in²
Hence, the surface area of the figure is equal to 88 in².