Question

A roof is in the shape of a triangular prism as shown below. You have enough paint to cover 25 square feet. If you use all the paint, how many square feet will be unpainted? (The bottom is not to be painted)

• A. $\text{10 sq ft}$
• B. $\text{7 sq ft}$
• C. $\text{20 sq ft}$
• D. $\text{15 sq ft}$

Answer 1

The correct option is B $\text{7 sq ft}$

The net of the triangular prism is as shown.


Area of rectangular face $\text{A = length × width}$
$\text{= 9 ft × 1.5 ft = 13.5 sq ft}$

Area of rectangular face $\text{B = length × width}$
$\text{= 9 ft × 1.5 ft = 13.5 sq ft}$

Area of triangular face $\text{C or D =}$
$\frac{1}{2}\times base\times height=\frac{1}{2}$$\text{× 2 ft × 2.5 ft = 2.5 sq ft}$

Surface area to be painted = area of rectangular face A + area of rectangular face B + area of triangular face C + area of triangular face $\text{D = 13.5 sq ft + 13.5 sq ft + 2.5 sq ft + 2.5 sq ft = 32 sq ft}$

Unpainted area $\text{= 32 sq ft – 25 sq ft = 7 sq ft}$

So, option D is correct.