Question

find the slant height of the pyramid. find the number of square inches that the puzzle pieces cover (surface area). find the number of cubic inches of space the completed puzzle will take up on a shelf. (volume).

Answer 1

Slant height of the pyramid

to find s we can use pythagoras on half triangle

`a^2+b^2=h^2`

where a and b are legs and h the hypotenuse

replacing

`\begin{gathered} 7^2+3.5^2=S^2 \\ 49+12.25=S^2 \\ S^2=61.25 \\ \\ S=\frac{7\sqrt[]{5}}{2}\approx7.83 \end{gathered}`

lenght of the slant height is 7.83inches

Surface area

we find the erea of each side of the pyramid, square(base) and 4 triangles

area of the square

`\begin{gathered} A=l* l \\ A=7*7 \\ A=49 \end{gathered}`

area of one triangle

`\begin{gathered} A=(b* h)/(2) \\ \\ A=(7*7)/(2) \\ \\ A=(49)/(2) \end{gathered}`

now sum the base and four triangles

`\begin{gathered} S=49+(49)/(2)+(49)/(2)+(49)/(2)+(49)/(2) \\ \\ S=147 \end{gathered}`

surface area of the pyramid is 147 square inches

Volume

we use the formula of the volume of the pyramid

`V=(A_b* h)/(3)`

where Ab is the area of the base (square=49in) and h is the height

replacing

`\begin{gathered} V=(49*7)/(3) \\ \\ V=(343)/(3)\approx114.33 \end{gathered}`

Volume of the pyramid is 114.33 cubic inches