Question

Find the surface area of the square pyramid (above) using its net (below). 3

Answer 1

Answer

33

Step-by-step explanation:

11 of the faces is a square.

\begin{aligned} \text{Area of a square} &= \text{side} \cdot \text{side}\\\\ &= 3 \cdot 3\\\\ &= {\blueD{9}} \\\\ \end{aligned}

Area of a square

​

 

=side⋅side

=3⋅3

=9

​

Hint #22 / 4

444 of the faces are triangles. Each triangle has the same base and height.

\begin{aligned} \text{Area of a triangle} &= \dfrac12 \cdot \text{base} \cdot \text{height}\\\\ &= \dfrac12 \cdot 3 \cdot 4\\\\ &= 6 \\\\ \end{aligned}

Area of a triangle

​

 

=

2

1

​

⋅base⋅height

=

2

1

​

⋅3⋅4

=6

​

The total area of these 444 triangles is 4 \cdot 6 = \greenD{24}4⋅6=244, dot, 6, equals, start color #1fab54, 24, end color #1fab54.

Hint #33 / 4

Let's add the areas we found to find the surface area.

\begin{aligned} \text{Surface area} &= \blueD{9}+ \greenD{24}\\\\ &= 33\\\\ \end{aligned}

Surface area

​

 

=9+24

=33

​

Hint #44 / 4

The surface area of this square pyramid is 333333 units^2

2

squared.