The exterior walls and roof of a barn are to be painted. The barn is in the shape of a rectangular prism, with an isosceles triangular prism for a roof. Calculate the total area to be painted.

There are two rectangles with lengths of 25 feet and widths of 10 feet while the other two rectangles have lengths of 55 feet and widths of 10 feet.

1. The area of a rectangle with a length of 25 feet and a width of 10 feet is,

[tex]\rm = 25 \times 10 = 250 \ square \ feet[/tex]

2. The area of two such rectangles is square feet is,

[tex]\rm = 250 \times 2 = 500 \ square \ feet[/tex]

3. The area of a rectangle with a length of 55 feet and a width of 10 feet square feet is,

[tex]= 55 \times 10 = 550 \ sqaure \ feet[/tex]

4. The area of two such rectangles square feet is,

[tex]\rm = 550 \times 2 = 1100 \ square \ feet[/tex]

The triangular prism has 2 triangles and 2 rectangles.

The triangles have base lengths of 25 feet and heights of 8 feet while the rectangles have lengths of 55 feet and heights of 14.8 feet.

5. The area of a triangle with a base length of 25 feet and a height of 8 feet square feet is,

[tex]\rm = \dfrac{1}{2} \times 25 \times 8\\\\= 4 \times 25 \\\\= 100 \ square \ feet[/tex]

6. The area of two such triangles is square feet is,

[tex]\rm = 100 \times 2 = 200 \ square \ feet[/tex]

7. The area of a rectangle with a length of 55 feet and a width of 14.8 feet square feet is,

[tex]= 55 \times 14.8 \\\\ = 814 \rm \ sqaure \ feet[/tex]

8. The area of two such rectangles is square feet is,

[tex]\rm = 2 \times 814 \\\\= 1628 \ square \ feet[/tex]

Therefore,

The total area to be painted is,

[tex]= 500+1100 +200+1628 \\\\= 3128 \rm \ square \ feet[/tex]

Hence, The total area to be painted is 3128 square feet.

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