We need to buy concrete floor paint for 1379 ft² and 163.2 feet lattice for the outside of the shed. Solution: To know how much paint we need to buy, we should know the total floor area to be painted.Think about the floor as four rectangles and a triangle. The area of the 31' by 36' main rectangle is 31*36 = 1116 ft² The area of the next largest rectangle is 10*21.5 = 215 ft² The area of the next to the smallest rectangle is 2.5*12 =30 ft² The smallest rectangle area is 3*4.5 = 13.5 ft² Lastly, ½*3*3 = 4.5 ft² is the area of the triangle.
The total floor area is the sum of the five areas: Area = 1116 + 215 + 30 + 13.5 + 4.5 = 1379 ft²
To know how much lattice is needed for the outside of the shed, we calculate for the perimeter by taking the sum of the length of each side. Starting on the right side then clockwise we have Perimeter = 36 + 31 + (36 - 21.5 - 3) + 4.2 + (10 - 3) + 21.5 + 3 + 4.5 + 3 + 2.5 + 12 + 2.5 + (31 + 10 - 4.5 - 12) = 163.2 feet
We would need to buy 163.2 feet lattice for the outside shed. Take note that the doors are included here. But if the two 3 feet doors are not included in the lattice, we will just subtract the length of the two doors from the perimeter. Thus, the lattice needed would only be 163.2 - 3*2 = 157.2 feet.
