Question

the picture is a model of a barn that is being built the bottom is a perfect cube with a square pyramid sitting on top the architect wants to paint the whole outside of the model (including the bottom) red, how much red paint will he need?

Answer 1

`\text{area}=184\text{ square cm}`

Step-by-step explanation

Step 1

to find the total area divide the figure

`\begin{gathered} \text{Area}=4\text{ squares+4 triangles} \\ \end{gathered}`

now, we need to find the area of the triangle

so, we need to find the hypotenuse of the triangle

`\begin{gathered} \text{hyp}^2=3^2+4^2 \\ \text{hyp}^2=9+16 \\ \text{hyp}^2=25 \\ \sqrt[]{\text{hyp}^2}=\sqrt[]{25} \\ \text{hyp}=5 \end{gathered}`

so, the height of the triangle is 5 cm

Step 2

let

side of the square=6

heigth of the triangle=5

base of the triangle=6

`\begin{gathered} \text{Area}=4\text{ squares+4 triangles} \\ \text{Area}=4(side^2)\text{+4 }((b\cdot h)/(3)) \\ \text{replace} \\ \text{Area}=4(6^2)\text{+4 }((6\cdot5)/(3)) \\ \text{area}=4(36)+4(10) \\ \text{area}=144+40 \\ \text{area}=184\text{ square cm} \end{gathered}`

I hope this helps you