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:

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

Therefore, the area of the auditorium:

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