1. **Problem statement:** Adam has built a garden shed composed of a rectangular prism base and a triangular prism roof. The base measures 4 m by 4 m by 2 m, and the triangular prism roof has a triangular face with a height of 3.5 m and base 4 m. Adam wants to paint the outside (walls and roof) but not the floor. One can of paint covers 4 m². 2. **Find the total surface area to be painted.** - Rectangular prism base surface area excluding the floor: The base has 4 vertical walls each 4 m wide and 2 m high. Total wall area = $4 \times 4 \times 2 = 32$ m². - Triangular prism roof surface area: The triangular face area = $\frac{1}{2} \times 4 \times 3.5 = 7$ m². There are two triangular faces, so total triangular faces area = $2 \times 7 = 14$ m². - The rectangular faces of the triangular prism (the roof sides): The length of the prism is 4 m (matching the base). The two rectangular sides each have area = base of triangle $\times$ length = $4 \times 4 = 16$ m² each. Total rectangular sides area = $2 \times 16 = 32$ m². - Total paintable surface area = walls + triangular faces + roof sides = $32 + 14 + 32 = 78$ m². 3. **Calculate the number of paint cans needed:** - Each can covers 4 m². - Number of cans = $\frac{78}{4}$. - Simplify with cancellation: $$\frac{\cancel{78}}{\cancel{4}} = 19.5$$ - Since Adam cannot buy half a can, he needs 20 cans. 4. **Calculate the total cost including 13% tax:** - Cost per can = 16.95. - Total cost before tax = $20 \times 16.95 = 339$. - Tax amount = $339 \times 0.13 = 44.07$. - Total cost including tax = $339 + 44.07 = 383.07$. **Final answers:** - a) Adam needs 20 cans of paint. - b) The total cost including tax is 383.07.