Answer:
a) 2899.33
b) 51
c) 1222
d) 14700
Step-by-step explanation:
a) Find out the area of all sides one by one and add it at the end
<u>Area of triangle at front + Area of triangle at the back</u>
Area of triangle = 1/2 x base x height + 1/2 x base x height
Area = 1/2 x 20 x 4 + 1/2 x 20 x 4
Area = 40 + 40
Area = 80
<u>Area of rectangle at front + Area of rectangle at back</u>
Area of rectangle = length x breadth + length x breadth
Area = 20 x 15 + 20 x 15
Area = 300 + 300
Area = 600
<u>Area of rectangle on both sides</u>
Area of rectangle = length x breadth x 2
Area = 45 x 15 x 2 = 1350
<u>Area of rectangle at the bottom</u>
Area of rectangle = length x breadth
Area = 45 x 20 = 900
<u>Area of rectangle at both sides of the roof</u>
Find the side length of the roof through the triangle
c² = a² + b²
c² = 4² + 10²
c = √116
c = 2√29
Area of rectangle = length x breadth x 2
Area = 45 x 2√29 x 2
Area = 969.33
<u>Add all areas</u>
Total surface area = 80 + 600 + 350 + 900 + 969.33
Total surface area = 2899.33
b)
1 paint can cover 57 square feet
x paints can cover 2899.33 square feet
1 : 57
x : 2899.33
Cross multiply
57x = 2899.33
x = 50.86 rounded off to 51
Therefore, 51 paint cans should be purchased to paint.
c)
1 paint costs $23.50
52 paints cost $x
1 : 23.5
52 : x
Cross multiply
x = 52 x 23.5
x = $1222
Therefore, the paint will cost $1222.
d)
Volume of cuboid = length x width x height
Volume = 20 x 45 x 15
Volume = 13500
Volume of pyramid = 1/3 x Base Area x Height
Volume = 1/3 x (20 x 45) x 4
Volume = 1200
Total Volume = 1200 + 13500
Total Volume = 14700
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