Question

7.) alex is tiling his entryway. the floor plan is drawn below.

if the cost of tile is $2.25 per square foot, how much will alex pay to tile his entryway?

Explanation:

Step1: Identify shapes and dimensions

The entryway is a trapezoid on top of a rectangle.

• Rectangle: height $h_1=12$ ft, width $w=9$ ft
• Trapezoid: top base $b_1=13$ ft, bottom base $b_2=9$ ft, height $h_2=27-12=15$ ft

Step2: Calculate area of rectangle

Use area formula $A_{rect}=w\times h_1$
$A_{rect}=9\times12=108$ square feet

Step3: Calculate area of trapezoid

Use area formula $A_{trap}=\frac{1}{2}(b_1+b_2)h_2$
$A_{trap}=\frac{1}{2}(13+9)\times15=\frac{1}{2}\times22\times15=165$ square feet

Step4: Find total area of entryway

Sum the two areas: $A_{total}=A_{rect}+A_{trap}$
$A_{total}=108+165=273$ square feet

Step5: Calculate total cost of tiling

Multiply total area by cost per square foot: $Cost=A_{total}\times2.25$
$Cost=273\times2.25=614.25$

Answer:

$\$614.25$