The surface area of the entire pyramid is 40 square units.
The triangles have base lengths of 4 units and heights of 3 units.
Step-by-step explanation:
Step 1:
To calculate the surface area of the pyramid, we must calculate the areas of all the 5 sides.
We divide the pyramid into 1 square and 4 triangles, find the areas individually and then sum them all up to calculate the surface area of the entire pyramid.
Step 2:
There are four triangles with base lengths of 4 units and heights of 3 units. To calculate a triangle's area we multiply [tex]\frac{1}{2}[/tex] with the product of the base length and it's height.
The area of 1 triangle [tex]= \frac{1}{2} (4)(3) = 6[/tex] square units.
The area of 4 such triangles [tex]= 4(6) = 24[/tex] square units.
Step 3:
The area of a square is the square of its side length.
The square has a side length of 4 units.
The area of the square base [tex]= 4^{2} = 16[/tex] square units.
The surface area of the entire pyramid is the sum of the areas of the 4 triangles and the square.
The surface area of the entire pyramid[tex]= 24+16 = 40[/tex] square units.
The surface area is 40 square units.
