We want to calculate the surface area of a square pyramid. Let's see the given measurements of the pyramid.

We can use a net to calculate the surface area of the pyramid. Let's see the net!

The net is made up of a square and four triangles. Let's calculate the area of each polygon separately, starting with the square.

A = s^{2}

Substitute

$s = 2$

A = 2^{2}

CalcPow

Calculate power

A = 4

The area of the square base is

4

square feet. Now let's take a look at the triangles. Notice that the sides of the pyramid are congruent triangles. This means that they have the same area. Let's substitute the measures of the sides into the formula for the area of a triangle!

A = \frac{1}{2} b h

SubstituteII

$b = 2$ , $h = 3$

A = \frac{1}{2} \cdot 2 \cdot 3

Multiply

A = 3

We found that the area of one triangle is

3

square feet. Since the triangles are congruent, the area of each triangle is

3

square feet. Now we have all the information that we need to find the total surface area of the square pyramid!

\underline{Total Surface Area} 4 + 3 + 3 + 3 + 3 = 16 ft^{2}

The total surface area of the square pyramid is

16

square feet.

Exercise