Question

A movable section of stage has the shape of an isosceles right triangle. You need to apply 2 coats of paint to all but the bottom. The paint covers approximately 80 square feet per quart. How many quarts of paint do u need to buy? The width is 12 18/25 ft height isc1 1 1/2 and length is 9 ft

Answer 1

Answer:

9 quarts of paint

Step-by-step explanation:

-Since, the bottom area is not painted, the total area would be the sum of the two isosceles faces and the two remaining rectangles.

#Area of Isosceles faces:

$A=0.5b\times \perp h, \ \perp h=11.5\ ft, \\\\2b=2\times\sqrt{(12.72^2-11.5^2)}=10.8712\\\\2A=2\times 0.5\times 10.8712\times 11.5\ ft\\\\=125.0188\ ft^2$

#Area of the two rectangles:

$A_1=lw\\\\=9\times 12.72\\\\=114.48\ ft^2\\\\A_2=lw, \ \ w=b=10.8712\\\\=9\times 10.8712\\\\=97.8408\\\\\therefore A=A_1+A_2\\\\=114.48+97.4808\\\\=212.3208\ ft^2$

#The total area to be painted is the sum of all faces:

$Total \ Area=125.0188+212.3208=\\\\=337.3396\ ft^2$

Since, the area would be covered twice and that 1 quart covers 80 sq ft. Let X be the number of quarts of paint:

$Area \ Covered= 2Area\\\\=2\times 337.3396\\\\=674.6792\ ft^2\\\\80 \ ft^2=1qt\\674.6792\ ft^2=X\\\\X=\frac{674.6792}{80}\\\\=8.43349\approx 9\ qts\ of \ paint$

Hence, you need to buy approximately 9 quarts of paint.