House surface area: Ralph is painting the barn, including the sides and roof....

[georg]

So this is the image. The question is:

[FONT=&quot](a) Ralph is painting the barn, including the sides and roof. He wants to know how much paint to purchase. What is the total surface area that he is going to be painting? Round to the nearest hundredth.[/FONT]
[FONT=&quot](b) If one paint can covers 57 square feet, how many paint cans should he purchase?[/FONT]
[FONT=&quot](c) If each paint can costs $23.50, how much will the paint cost?




I'm only really having problems finding the surface area, because it affects the rest of these questions.

This is the work I've done, but it's wrong. So what do I have to do to fix it?


[/FONT]
(A) Total Surface Area
Rectangular Prism
2(wl + hl + hw)


2 (45 x 20 + 15 x 20 + 15 x 45) = 3750


Triangular Prism
L + 2B
h(a + b + c) + Ab


45(15 + 20 + 15) + 4 x 20
2250 + 80
2330




Total surface area - 3750 + 2330


6080


(B) Paint Cans


6080 / 57


106.6 or 107 paint cans
I had to divide the total surface area with how much area one paint can would cover.


(C) Price


If each paint can costs $23.50, and Ralph buys 107 paint cans, he will spend $2,514.50

 

[Harry_the_cat]

So this is the image. The question is:

(a) Ralph is painting the barn, including the sides and roof. He wants to know how much paint to purchase. What is the total surface area that he is going to be painting? Round to the nearest hundredth.
(b) If one paint can covers 57 square feet, how many paint cans should he purchase?
(c) If each paint can costs $23.50, how much will the paint cost?




I'm only really having problems finding the surface area, because it affects the rest of these questions.

This is the work I've done, but it's wrong. So what do I have to do to fix it?



(A) Total Surface Area
Rectangular Prism
2(wl + hl + hw)


2 (45 x 20 + 15 x 20 + 15 x 45) = 3750


Triangular Prism
L + 2B
h(a + b + c) + Ab


45(15 + 20 + 15) + 4 x 20
2250 + 80
2330




Total surface area - 3750 + 2330


6080


(B) Paint Cans


6080 / 57


106.6 or 107 paint cans
I had to divide the total surface area with how much area one paint can would cover.


(C) Price


If each paint can costs $23.50, and Ralph buys 107 paint cans, he will spend $2,514.50

You are right in saying that the barn is made up of a rectangular prism and a triangular prism.

Now pretend you have a paintbrush in your hand. (Put yourself in the real-world problem - sounds silly but it really does help!)

Are you painting all the surfaces of the rectangular prism and triangular prism? No you're not.

So forget the formulae and look at each surface to paint separately. The walls are basically 4 rectangles. The roof structure is made up of two rectangles and two triangles. Find them separately and add them up. (Hint: You will need to find the hypotenuse of the appropriate right angled triangle. Think Pythagoras.)

Give it another go.