Question

name: _ date: _ area of composite figures application / 37 1. two coats of paint are to be applied to this wall. one can of paint costs $43.99 before tax and covers 45 m². 17 ft 22 ft 40 in. 40 in. 29 ft a) determine the total surface area to be covered by two coats of paint, to the nearest tenth of a square metre. (1ft = 0.3048m) 8a b) determine the number of cans of paint needed and the total cost, including 13% sales tax. 2a

Explanation:

Step1: Calculate the area of the rectangle part of the wall

The rectangle has dimensions $29$ ft by $17$ ft. The area of a rectangle is $A = l\times w$. So, $A_{rectangle}=29\times17 = 493$ square - feet.

Step2: Calculate the area of the triangular part of the wall

The base of the triangle is $29$ ft and the height of the triangle is $22 - 17=5$ ft. The area of a triangle is $A=\frac{1}{2}bh$. So, $A_{triangle}=\frac{1}{2}\times29\times5=\frac{145}{2}=72.5$ square - feet.

Step3: Calculate the area of one window

The side - length of each window is $40$ inches. First, convert inches to feet. Since $1$ foot = $12$ inches, $40$ inches=$\frac{40}{12}=\frac{10}{3}$ feet. The area of one square - shaped window is $A_{window}=(\frac{10}{3})^2=\frac{100}{9}\approx11.11$ square - feet. The area of two windows is $2\times\frac{100}{9}=\frac{200}{9}\approx22.22$ square - feet.

Step4: Calculate the area of the wall to be painted

The area of the wall before conversion is $A_{wall}=A_{rectangle}+A_{triangle}-A_{windows}=493 + 72.5-22.22=543.28$ square - feet.

Step5: Convert the area from square - feet to square - meters

Since $1$ ft = $0.3048$ m, $1$ square - foot=$(0.3048)^2$ square - meters. So, $A_{wall - m}=543.28\times(0.3048)^2$.
$A_{wall - m}=543.28\times0.09290304\approx50.4$ square - meters.
The area to be covered by two coats of paint is $2\times50.4 = 100.8$ square - meters.

Step6: Calculate the number of cans of paint needed

One can of paint covers $45$ square - meters. The number of cans, $n=\frac{100.8}{45}\approx2.24$. Since we can't buy a fraction of a can, we need $3$ cans of paint.

Step7: Calculate the cost of the paint before tax

The cost of one can is $\$43.99$, so the cost of $3$ cans before tax is $3\times43.99=\$131.97$.

Step8: Calculate the sales tax

The sales tax rate is $13\%$ or $0.13$. The amount of tax is $0.13\times131.97=\$17.16$.

Step9: Calculate the total cost

The total cost is $131.97 + 17.16=\$149.13$.

Answer:

a) $100.8$ square - meters
b) Number of cans: $3$, Total cost: $\$149.13$