$6$ . A storage shed in the shape of an isosceles triangular prism is to be painted (note the diagram). The paint is sold in cans that each cover $40 \mathrm{ft}^{2}$ and cost $\$ 16.50$ . How much will it cost to give the shed TWO coats of paint? YOU WILL NOT NEED TO PAINT THE BOTTOM SIDE OF THE PRISM. ( $5$ )

Full solution

6

. A storage shed in the shape of an isosceles triangular prism is to be painted (note the diagram). The paint is sold in cans that each cover

40 \mathrm{ft}^{2}

and cost

\$ 16.50

. How much will it cost to give the shed TWO coats of paint? YOU WILL NOT NEED TO PAINT THE BOTTOM SIDE OF THE PRISM. (

5

)

Identify Surfaces: Identify the surfaces to be painted: two triangular faces and three rectangular faces.
Calculate Triangle Area: Calculate the area of one triangular face using the formula for the area of a triangle: $A = \frac{1}{2} \times b \times h$ . Assume the base is $'b'$ and the height is $'h'$ .
Calculate Rectangle Area: Calculate the area of one rectangular face using the formula for the area of a rectangle: $A = l \times w$ . Assume the length is $l$ and the width is $w$ .
Calculate Total Area: Add the areas of all the faces to get the total surface area to be painted. Remember, we don't paint the bottom face. $\newline$ Total area = $2 \times (\text{area of triangular face}) + 3 \times (\text{area of rectangular face})$ .
Multiply Total Area: Multiply the total area by $2$ to account for the two coats of paint required.
Divide by Coverage Area: Divide the total area to be painted by the coverage area of one can of paint to find out how many cans are needed.
Round Up to Nearest Whole: Since the number of cans might not be a whole number, round up to the nearest whole number because you can't buy a fraction of a can.
Calculate Total Cost: Multiply the number of cans $n$ by the cost per can $c$ to find the total cost $n \times c$ .