Question

i really need help pleaseThe floor plan of a school auditorium is shown. What is the area of the auditorium?

Answer 1

The area of the auditorium is given by:

Will be the area of the blue rectangle minus the area of the red triangles, so:

The area of the rectangle is:

`\begin{gathered} Ar=w\cdot l \\ where\colon \\ w=32 \\ l=13+3=16 \\ Ar=512ft^2 \end{gathered}`

The area of each triangle is:

`\begin{gathered} At=(b\cdot h)/(2) \\ where\colon \\ b=(32-20)/(2)=6 \\ h=3 \\ so\colon \\ At=(6\cdot3)/(2) \\ At=(18)/(2) \\ At=9ft^2 \end{gathered}`

Therefore, the area of the auditorium:

`\begin{gathered} A=Ar-2At \\ A=512-2(9) \\ A=512-18 \\ A=494ft^2 \end{gathered}`